Before I go any further, I want to say that even though it may seem as though other players' bios are out of this world, your bio should be uniquely efficient for you. Sometimes people fill up their bios with lots of background and a bunch of in-depth stuff, which is great, but if that's not the type of bio that suits your needs, don't feel the need to succumb to popular bio types.
If you want to improve your character's biography, a great way is to, first, list the basics, the necessities- generally, things you want people to know immediately about the character. (I mean, that's kind of how real-life interaction works, right? You learn the simple things about someone, (age, gender) before you discover some of the deep things that make up a large portion of their background. (backstory, origins, fears, strengths, weaknesses, etc.) It's quite apt, actually, but nevermind that, I'm getting off-topic.)
If you want to go into further detail, like many of the generous people above have mentioned, try creating a backstory, or "story" for your character. Maybe list some of their darkest secrets (unless, of course, you want it to stay a secret) or something worth knowing about your character, or something very personal to their character. You could even record a theme song for your character. I could go on, and I could give you a few more examples, but I would be repeating many of the answers above.
Just try to get creative with it. Let your imagination run wild, and write what comes naturally.
Good luck!
