If you call someone erudite, that means they show great learning. After you've earned your second Ph.D., you will be truly erudite.
Erudite is from Latin verb erudire, "to teach," which comes from rudis for "raw, unskilled, ignorant" (the source of our word rude). If you bring someone out of a raw state, you educate them, so someone who is erudite is very educated indeed (and perhaps a bit of a showoff). You can say either ER-oo-dite or ER-yoo-dite; the second one, being a bit harder to say, can seem a bit more erudite.