John Donne gives us the first hint of the poem's meaning with the title. Alchemy was a precursor to modern day chemistry. Those who performed alchemy believed they could change substances into other substances, most notably changing worthless substances into gold. Of course, no one was ever able to accomplish their goals. So alchemy is seen as something that was striven for, but never obtained.
The speaker of the poem tells the audience that he has loved passionately, but that he still does not understand love. He feels that no one can ever understand love to the point of being able to explain it completely. He states, "should I love, get, tell, till I were old, I should not find that hidden mystery."
In the second stanza, the speaker goes on to say, "That loving wretch that swears 'tis not the bodies marry, but the minds," is still not completely grasping or articulating the true nature of love. He points a finger at these people, saying they, "hope not for mind in women." This is the speaker saying that they do not want intelligent women, just women who have, "at their best, sweetness and wit."
Ultimately it seems John Donne's speaker has little patience for those who claim they can write and explain love because he feels that those same men would never love a woman with any true depth.