Something innumerable can't be counted — there are just too many, like the stars in the sky. Innumerable things are infinite.
Things that are countless, multitudinous, myriad, numberless, uncounted, or unnumerable are also called innumerable: you couldn't count them if you tried. There are a lot of countries in the world, but they aren't innumerable. On the other hand, the number of drops in the ocean is definitely innumerable. And if you wanted to be really nice, you'd say "Her charms are innumerable!" Even though you could probably count all of her good qualities.