To show forth thy loving-kindness - To celebrate thy mercy; thy goodness; thy love.
In the morning - That is, there is a fitness in doing this in the morning; or, there are special reasons why we should do this at that time.
(a) We have been preserved through the dangers of the night; dangers when we were asleep, unconscious, and defenseless.
(b) Life is then, as it were, a new gift - for we are raised from "the image of death" - sleep - and we should regard life then "as if" we had been raised from the dead.
(c) To praise God in the morning will have a good influence on us, in promoting cheerfulness; in making us benignant and kind; in preparing us for the toils and trials of the day.
There is no better preparation for a day, in view of its burdens, cares, toils, and trials, than a thankful, cheerful mind in the morning. He who begins a day with a sour, a morose, a complaining, an irritable spirit - who has been preserved through the night, and sees nothing to be thankful for in the morning - will be a miserable man through the day, and will make all miserable around him. He who sees nothing to be thankful for in the morning will see nothing to hope for in the day; he who has no gratitude for the past, will have no bright anticipations of the future.
And thy faithfulness - Faithfulness in the laws of nature; in thy promises; in thy character: in thy providential dealings with people.
Every night - Margin, in the nights." The reference is to the return of evening; and the meaning is, that it is a good thing, or that it is appropriate to contemplate the faithfulness of God at the close of every day.
(a) The mind is then calm, after the toils of the day are over.
(b) The time - evening - its stillness - its twilight - its approaching darkness - all is favorable for reflection.
(c) There is much in every day to be thankful for, and it is well to recall it at night.
(d) It has a happy effect on the mind when we are about to lie down to rest, to recall the mercies of God; to reflect on what he has done for us; to gather, from his kindness in the past, lessons of confidence and hope for the times to come.
We lie down at night more calmly in proportion as we are disposed at the close of a day to think of the mercies which we have received at the hand of God; and the recalling of those mercies to remembrance with the voice, and with instruments of praise, is always an appropriate mode of closing a day.

To show forth thy loving-kindness - חסדך chasdecha, thy abundant mercy, in the morning - that has preserved me throughout the night, and brought me to the beginning of a new day: and thy faithfulness in the night, that has so amply fulfilled the promise of preservation during the course of the day. This verse contains a general plan for morning and evening prayer.

To shew forth thy lovingkindness in the (b) morning, and thy faithfulness every night,
(b) For God's mercy and fidelity in his promises toward his, bind them to praise him continually both day and night.

To show forth thy lovingkindness in the morning,.... God has shown forth his lovingkindness in Christ, and Christ has shown it in a ministerial way; and saints should show it forth also with their lips, to warm the hearts of one another, and encourage distressed minds; this should be a part, and a considerable one, of their thanksgiving and praise; as it will appear to be, when the objects of it are considered, not angels, but men, and these the worst and vilest; the instances of it in election, redemption, calling, adoption, and eternal life; and the freeness, earliness, and immovableness of it; and this is to be done in the "morning", not of the sabbath day only, but every other day, giving praise and thanks for the mercies of the night. Jarchi interprets it of the time of salvation:
and thy faithfulness every night: or "in the nights" (b); not the night and goings out of the sabbath only, so Arama; but every other night, observing and declaring the faithfulness and truth of God in his counsels and covenant, in his word and promises, and in the preservation of his people, and the continuance of favours to them; particularly praising his name, and giving thanks unto him openly for the mercies of the day past: morning and night being mentioned may have some respect to the morning and evening sacrifices; and may signify that our sacrifices of praise should be offered up to God continually, Hebrews 13:15.
(b) "in noetibus", Pagninus, Montanus, Tigurine version, &c.

in the morning, . . . every night--diligently and constantly (Psalm 42:8).
loving kindness--literally, "mercy."
faithfulness--in fulfilling promises (Psalm 89:14).