This poem, written about 400 years ago, uses some wording that we wouldn't use today. Specifically, the words "prove" and "sports" have slightly different meanings for the modern reader than they did for Ben Jonson's readers. "Prove" means to demonstrate something's existence or truth. The poem's speaker wants to demonstrate the existence of "the sports of love." "Sport" here means, not physical exertion, but its archaic meaning of a source of entertainment or amusement. The speaker, then, is encouraging Celia, his love interest, to demonstrate how much enjoyment they can derive from "love." That the "love" referred to is intimate physical love is clear from the rest of the poem. The speaker discounts "fame and rumor," suggesting that if they were caught together and their reputations ruined, it wouldn't really matter. Nevertheless, he feels it would be quite easy to keep their affair secret from others in the "household" and even from him who was "removed by our wile," probably Celia's husband. The reference to stealing "love's fruit" suggests that Celia belongs to another, also pointing to the physical nature of the proposed foray into "love."

The phrase "while we can" is expanded on in lines 3 - 9 where the speaker explains that they should seize the moment. This argument is the 17th century version of the modern phrase "YOLO," or "you only live once." The speaker seems to believe he and Celia have the perfect opportunity to act on their love, perhaps because her husband is away, and that they shouldn't let the moment escape. Although the language used is a bit dated, the thoughts expressed couldn't be more modern. 

Ben Jonson wrote two different poems both entitled "Song: To Celia." You can read the other one at the link below.