Mario, in of himself, is not that great a character. He's world-famous, easily recognizable, and stars in some superb video games, but if you asked me to talk about who the character is, I'd falter.
Here's a quick list of things that are really off the top of my head (no really, I'm just now trying to think these up) about Mario:
He goes "yahoo" a lot.
He's very upbeat.
He's always willing to save a princess from dragon turtle things.
He likes to go-cart.
He once had a talking, water-spraying jet pack for a sidekick.
He gets along well with dinosaurs.
Different types of plant life do different things to his body.
That's a pretty bland character, because there just isn't much personality there. Mario doesn't ever really say anything besides "okie-dokie," "let'sa go," or "it'sa me!" Luigi, on the other hand, has a lot more depth, since we know he's a bit of a coward, but still willing to walk into danger. He's fiercely loyal to his brother. He tends to be a bit clumsy, and acts goofy at strange times. He can be a little lazy, and doesn't really get into the pomp of ceremonies thrown by the princess ("What, another cake? Wake me when this kingdom discovers booze.")
Now, there are some small exceptions to this rule, and they tend to come in the RPGs featuring Mario.