Nature herself was proud of his designs And joy'd to wear the dressing of his lines (47-48)
Shmoop really likes the idea of nature wearing poetry like people wear clothes. In these terms, Shakespeare is basically Armani.
As, since she will vouchsafe no other Wit The merry Greek, tart Aristophanes, Neat Terence, witty Plautus, now not please But antiquated and deserted lie (51-54)
Nature, it seems, likes to play favorites. Here she is portrayed unilaterally rejecting other poets in favor of Shakespeare's descriptions.
Yet must I not give Nature all: thy art My gentle Shakespeare, must enjoy a part (55-56)
Shakespeare's art as opposed to his natural talent gets "a part" of the credit, but Jonson seems to gush much more over nature.
For though the Poet's matter, Nature be His Art doth give the fashion […] (57-58)
The word "matter" here works two ways: one, meaning the poet's subject matter is Nature but his art gives those words structure and substance, and two, the poet's substance, or what makes a person a poet, is a natural gift, but only with hard work does that gift mature and produce great poetry.
For a good Poet's made as well as born (64)
Truer words never spoken. Three cheers for Jonson, amirite?