To me, an Athlete is someone who consistently, and regularly, participates in athletic activity specifically with the intent to get better and to push themselves. Someone who power-walks at the park 3 times a week probably isn't an Athlete. Someone who runs and cycles 3 times a week with a goal to get a little faster or ride/run a little farther might be an athlete. To me it's sort of like "photographer" or "artist". Lots of folks in those categories like to tell other people that they aren't "that". But unless you put the "pro" in front of it, if it's something that you do regularly, strive to improve at, and take seriously; then I think you can call yourself "That".
Interestingly though, I give that definition, and I fit that definition, but I don't call myself an "Athlete".
Sometimes folks define it as competing. And I guess that makes sense, too. You're an athlete if you take your skills, abilities, and training; and compete with others using those skills and ability and training.
I think if an athlete only defines someone who is really good, or is professional, et al, then it eliminates the need for all of the qualifiers. "Competitive athlete", "Professional athlete", etc. Surely if we're separating those people, then there must be another class of plain old "Athlete"?