If you are earnest, it means you are serious about something. Your parents might not want you to drop out of school to follow some fly-by-night dream, but if you're earnest about wanting a career in show biz, they'll support you.
If you are earnest, you pursue your purpose in a steady, sincere, and eager way. The phrase in earnest uses earnest as a noun, as in, "Once you stop fooling around and start studying in earnest, you'll find you learn the material quickly." Oscar Wilde's classic play, "The Importance of Being Earnest," plays on the fact that Ernest is also a man's name.