Watts published this hymn under the subject:
Our frail Bodies, and God our Preserver
Isaac Watts (1719). The Psalms of David, book II, hymn XIX.
The stanza in the question consists of two metaphors. First, the human body is compared to a clockwork mechanism, containing many springs, all of which are vital for its operation. Second, the human body is compared to a harp of many strings, all of which must be tuned correctly for the instrument to play in harmony.
Both metaphors portray the human body as a delicate mechanism that requires constant attention, the implication being that God is our maintenance operator:
But ’tis our God supports our frame,
The God that built us first:
Salvation to th’ Almighty name
That reared us from the dust.