Composition Date:
ca. 1643-47 (White 254).
Mean = lowly, humble, average.  Bradstreet is claiming that since she is a woman, she is unable to write about the great events that concern male poets - "of Wars, of Captains, and of Kings, / Of Cities founded, Common-wealths begun."  This seems to be a reference to The Aeneid by Virgil, which is an ancient epic describing the founding of Rome.  But she does want to write about the things she does know.
Bartas: Guillaume du Bartas (1544-90), French poet.
She will do what she is able to do.
Practice ("art") can't make up for the lack of talent, or for the fact that nature made her a woman.
"that fluent sweet-tongued Greek": Demosthenes, an ancient Athenian who overcame a speech impediment by practicing speaking with rocks in his mouth. Became one of Athens' greatest orators.
Critics ("each carping tongue") say a needle fits her hand better than a pen, i.e., she should tend to her knitting and be content doing 'women's work'.
Even if she writes beautiful poetry, others will claim that she plagarized it. Such accusations were actually made about the work of Fredrecik Douglass, the runaway slave who became an Abolitionist speaker.
Calliope: muse of heroic or epic poetry. If the muses were female, then women should be able to write.
She defers to male superiority, but insists that she has her place also. Men need not feel threatened by her work.