The press - The crowd, the multitude of people. Jesus was probably in the large open area or hall in the center of the house. See the notes at Matthew 9:2. The people pressed into the area, and blocked up the door so that they could not have access to him.
They uncovered the roof where he was - See the notes at Matthew 9:2.
When they had broken it up - When they had removed the awning or covering, so that they could let the man down. See the notes at Matthew 9:2.

They uncovered the roof - The houses in the east are generally made flat-roofed, that the inhabitants may have the benefit of taking the air on them; they are also furnished with battlements round about, Deuteronomy 22:8; Judges 16:27; and 2-Samuel 11:2, to prevent persons from falling off; and have a trap door by which they descend into the house. This door, it appears, was too narrow to let down the sick man and his couch; so they uncovered the roof, removed a part of the tiles; and having broken it up, taken away the laths or timber, to which the tiles had been attached, they then had room to let down the afflicted man. See Luke 5:19, and on Matthew 10:27 (note); Matthew 24:17 (note).

And when they could not come nigh unto him for the press, they uncovered the roof where he was: and when they had broken [it] up, they (c) let down the (d) bed wherein the sick of the palsy lay.
(c) They broke up the upper part of the house which was made simply, and let down the man that was sick from paralysis into the lower part where Christ preached, for they could not come before Christ in any other way.
(d) The word signifies the poorest kind of bed, upon which men used to lay down at noon, and at such other times to refresh themselves; we call it a couch.

And when they could not come nigh unto him for the press,.... To the room where Jesus was, nor into the house, nor even to the door, the crowd about it was so great,
they uncovered the roof where he was. The Arabic version reads it, "they went up to the roof"; and the Persic thus, "they carried him up upon the roof". The place where Christ was, seems to be an upper room; for in such an one the Jewish doctors used to meet, and discourse together about religious matters; see Acts 1:13. Though some think this was a mean house in which Christ was, and had no upper room, but the ground floor was open to the roof, through which the man, sick of the palsy, was let down on his bed to Christ; and the rather, because the people crowded about the door to get in, and there was no room to receive them, no not about it: but even from this circumstance it seems most reasonable, that there was an upper room in which Christ was, and at a window in which he might preach to the people, with much more convenience, than at, or about the door, where they were pressing: for, certain it is, that he did preach the word to them, Mark 2:2, and many instances may be given of the above mentioned doctors, whose usages, when indifferent, and not sinful, might be complied with by Christ, as these were, of their meeting and conversing together in upper rooms. Instead of many, take the few following (a):
"It happened to Rabban Gamaliel, and the elders, who were sitting "in an upper room in Jericho", that they brought them dates, and they did eat, &c,''
Again (b),
"these are some of the traditions which they taught, "in the upper chamber" of Hananiah ben Hezekiah, ben Garon.''
So it is likewise said (c), that
"R. Tarphon, or Tryphon, and the elders, were sitting "in the chamber" of the house of Nithzah, in Lydda, and this question was asked before them, is doctrine greatest, or practice greatest?''
Once more (d),
"the elders of the house of Shammai, and the elders of the house of Hillell, went up, "to the upper chamber" of Jochanan ben Bethira, and said, that the Tzitzith, or fringes, had no measure, &c.''
Now, over this upper room, was a flat roof, with battlements about it; for so the Jews were obliged to build their houses, Deuteronomy 22:8, to which they had a way of going to and from, both within and without side their houses; See Gill on Matthew 24:17. Hence we so often read (e) of , "the way of the roofs", in distinction from "the way of the doors"; by which they entered into their houses, and by which means, things might be carried from a court to a roof, and from a roof to a court; about which the doctors dispute, saying, that on a sabbath day (f),
"it is forbidden to ascend and descend from the roofs to the court, and from the court to the roofs; and the vessels, whose abode is in the court, it is lawful to move them in the court, and which are in the roofs, it is lawful to move them in the roofs.--Says Rabbi, when we were learning the law with R. Simeon at Tekoah, we brought up oil, and a confection of old wine, water, and balsam, from roof to roof, and from roof to court, and from court to court, and from the court to a close, and from one close to another, till we came to the fountains, in which they washed. Says R. Judah, it happened in a time of danger, and we brought the book of the law from court to roof, and from roof to court, and from court to a close, to read in it.''
Now, in these roofs, there was a door, which they call, , "the door of the roofs" (g); now when they had brought up the sick man to the roof of the house, by a ladder fastened on the outside, which was common (h); they took up this door, and let him down in his bed into the room where Jesus was: and because they wrenched the roof door open with violence, therefore it is said,
and when they had broken it up, they let down the bed wherein the sick of the palsy lay: opening the door, and perhaps taking up the frame of it, and removing some tiles about it, to make the way wider, they let down with ropes, the bed, and the man on it, together. The Persic version thus renders it, "and the paralytic man being put upon a bed, at the four corners of the bed so many ropes being fastened, they let him down through a window to Jesus, into the place where he was sitting"; which is rather a paraphrase, or exposition of the words, than a translation.
(a) T. Bab. Beracot, fol. 37. 1. (b) T. Bab. Sabbat, fol. 12. 1. & Misn. Sabbat, c. 1. sect. 4, (c) T. Bab. Kiddushin, fol. 40. 2. Vid. T. Hieros. Pesachim, fol. 30. 2. & T. Bab. Sanhedrin, fol. 74. 1. (d) T. Bab. Menachot, fol. 41. 2. Vid. Targum in Cant. iii. 4. (e) T. Pesach. fol. 92. 1. Moed. Katon, fol. 25. 1. Cetubot, fol. 10. 2. Gittin, fol. 81. 1. Bava Metzia, fol. 88. 1, in 117. 1. (f) T. Bab. Erubin, fol. 91. 1. & Hieros. ib. fol. 25. 3. (g) T. Hieros. Erubin, fol. 26. 2. (h) Gloss. in T. Bab. Bava Metzia, fol. 117. 1.

And when they could not come nigh unto him for the press--or, as in Luke (Luke 5:19), "when they could not find by what way they might bring him in because of the multitude," they "went upon the housetop"--the flat or terrace-roof, universal in Eastern houses.
they uncovered the roof where he was: and when they had broken it up, they let down the bed--or portable couch
wherein the sick of the palsy lay--Luke (Luke 5:19) says, they "let him down through the tilling with his couch into the midst before Jesus." Their whole object was to bring the patient into the presence of Jesus; and this not being possible in the ordinary way, because of the multitude that surrounded Him, they took the very unusual method here described of accomplishing their object, and succeeded. Several explanations have been given of the way in which this was done; but unless we knew the precise plan of the house, and the part of it from which Jesus taught--which may have been a quadrangle or open court, within the buildings of which Peter's house was one, or a gallery covered by a veranda--it is impossible to determine precisely how the thing was done. One thing, however, is clear, that we have both the accounts from an eye-witness.

They uncovered the roof - Or, took up the covering, the lattice or trap door, which was on all their houses, (being flat roofed.) And finding it not wide enough, broke the passage wider, to let down the couch.