twelve baskets - Baskets belonging to the disciples, in which they carried their provisions, or, perhaps, belonging to some of the multitude.
Fragments - Broken pieces of the bread that remained.

Twelve baskets - These were either the baskets used by the disciples, see Matthew 14:20, or baskets belonging to some of the multitude, who might have brought some with them to carry provisions, or other things necessary for the sick, whom they brought to Christ to be healed.

And they took up twelve baskets full of the fragments,.... Of the broken pieces of bread, after all had eaten, and were satisfied:
and of the fishes; what remained of them:, for though there was but one loaf for a thousand persons and more, and two small fishes to be divided among five thousand and more: yet, through the wonderful power of Christ increasing both, as they were distributing and eating, there was enough of both for them all, and such a quantity of each left as filled twelve baskets.

And they took up twelve baskets full of the fragments, and of the fishes--"Therefore (says John 6:13), they gathered them together, and filled twelve baskets with the fragments of the five barley loaves, which remained over and above unto them that had eaten." The article here rendered "baskets" in all the four narratives was part of the luggage taken by Jews on a journey--to carry, it is said, both their provisions and hay to sleep on, that they might not have to depend on Gentiles, and so run the risk of ceremonial pollution. In this we have a striking corroboration of the truth of the four narratives. Internal evidence renders it clear, we think, that the first three Evangelists wrote independently of each other, though the fourth must have seen all the others. But here, each of the first three Evangelists uses the same word to express the apparently insignificant circumstance that the baskets employed to gather up the fragments were of the kind which even the Roman satirist, JUVENAL, knew by the name of cophinus, while in both the narratives of the feeding of the Four Thousand the baskets used are expressly said to have been of the kind called spuris. (See Mark 8:19-20.)

Full of the fragments - of the bread.