One obvious thematic idea is to face life's limitations (in this case, separation from a loved one) with strength. He is instructing his wife to disregard sadness by forbidding her to mourn. Why? Because their love is so strong, and so infinite, it really isn't a separation at all, but an "expansion" (stanza 6, ln. 21). Donne famously makes use of a "conceit" in this poem, which is an extended or exaggerated metaphor. In this poem, the speaker's the love that he and his wife share with twin compasses (the type with two "legs", whereby one remains fixed in one spot and the other moves around it). Yet another theme would suggest the power of the human spirit - especially relating to love and the power of family ties.
John Donne wrote the poem "A Valediction: Forbidding Mourning" for his wife before leaving on a trip. In it, scholars have found allusions to religious belief, to death, and to science. On the surface, though, he is telling his wife not to be sad because he is leaving. Their love is not like that of ordinary people, the "dull sublunary lovers." He says that these kinds of lovers can't stand to be apart because their love is based on appearances, on physical things, on "care less eyes, lips and hands to miss."
The love shared by Donne and his wife is higher than this. Theirs is a spiritual love. They are as one soul, so that where one goes the other is there as well in spirit. So sadness and tears at parting are not appropriate for them. Their love will grow from the anticipation of reuniting.
See the links below for a discussion of other themes in the poem.