Poets pack a lot of meaning / emotion into their words — you could think of them as “full” of the stuff that makes up life, like a pregnant woman is more literally filled with another life.
There are apparently two independent derivations of the word "pregnant" (though the roots may join), confusingly, both adjectives. Other than "with child", there is:
"convincing, weighty, pithy," late 14c., "cogent, convincing, compelling" (of evidence, an argument, etc.); sense of "full of meaning" is from c. 1400. According to OED from Old French preignant, present participle of preindre "press, squeeze, stamp, crush," from earlier priembre, from Latin premere "to press, hold fast, cover, crowd, compress" (from PIE root per- (4) "to strike").*
Probably the most common use of this meaning for "pregnant" in English is a "pregnant pause"; which are the points during speech where you pause for effect.