Donne's 17th "Holy Sonnet" can be paraphased to determine its obvious "meaning," but it can also be analyzed to explore its effectiveness as a poem. The poem was almost certainly written in response to the death of Donne's own wife, who passed away at age 33 after having just given birth to their twelfth child.
Donne opens the poem by saying that his wife ("she whom I loved")
hath paid her last debt
To Nature" (1-2)
In other words she has died, and although he speaks of his affection for her in the past tense ("loved"), the poem's very existence implies his continuing love for her. She has "paid her last debt / To Nature" (a standard phrase for dying, suggesting that we all live on borrowed time).
She can no longer do herself nor him any earthly "good" (2), since her spirit has been taken up into heaven prematurely and unexpectedly (3). Therefore, the speaker vows to focus his mind entirely on "heavenly things" (4), including his wife but including much else. Her death has reminded him of the mortality of himself and of all living things, and so he is in a properly meditative state of mind. Ironically, her death has thus done him some "good" (2) by making him direct his thoughts to heaven.
Even when his wife was still alive, the speaker's admiration for her whetted his appetite for seeking God (5-6). Her goodness reflected the goodness of her creator, and thus her presence inspired the speaker to want to seek out the divine source of that goodness, just as we can follow a stream to its source (6).
However, even though the speaker, thanks in part to his wife's influence on him, has found God, and even though God has helped slake some of his thirst for God's love, he still feels thirsty for even more love from God (7-8).
These lines are typical of much of the phrasing of the Holy Sonnets, because they show the speaker directly addressing God, as if in prayer. Likewise, the next line shows another characteristic of these poems -- the speaker's tendency to ask questions, including questions concerning himself:
. . . why should I beg more love, whenas [that is, when] thou
Dost woo my soul, for hers offering all thine [?] (10-11)
In other words, why does the speaker seek more love, when God offers infinite love in exchange for the necessarily limited (because mortal) love of the speaker's wife?
The final four lines of the poem suggest that God is indeed a jealous God, capable even of feeling "fear" (11) that the speaker may not only love "saints and angels" (which are "things divine" , but which are also inappropriate subsitutes for God) but that the speaker may also give his love to the unholy trinity of the world, the flesh, and the devil (14).
This closing idea that God might feel "fear" of losing the speaker's love may seem surprising, but Donne's poems are often surprising. The phrasing here suggests the intensity of God's love for mankind -- a love so intense that he was willing to sacrifice his own son to redeem fallen humanity. The speaker, at the beginning of the poem, emphasizes the loss of a loved one of his own, but the final four lines of the poem suggest that God himself is capable of fearing a similar loss.
God feels what Donne calls, in the kind of paradoxical language typical of his poems, a "tender jealousy" (13) -- a jealousy rooted in love, concern, gentleness, and infinite caring.
For a superb edition of The Holy Sonnets, see the ongoing Variorum Edition of Donne's poems (Gary Stringer, general editor)