Why Do People Leave Home, And Seek Adventure?
There's lots of reasons. They've heard tales of great adventurers and want to become one. They're seeking riches. They're seeking riches in order to marry the girl they love. They're out to revenge something, or prove something. They are talented, and easily bored. They seek fame. They seek excitement. They seek travel. Their best friend wanted to be an adventurer, so they went with him. Their family expected it of them. They are looking for someone. They are looking for something. They want to be written into the annals of history. They are desperately trying to find the answer to averting something. Everyone they know is dead and their only profession is violence. They're on the run. They really, really, really like killing things. They don't really know why they fell into this life, it was just easier than the alternatives (and they're good enough at it not to die). It's a job, like any other. Society must be defended. Someone must fight the good fight. Village soothsayer told me to. Priest/father/lover/old tree told me to. They seek power. I'm being paid to do this. I was threatened/blackmailed/forced/mind-controlled/convinced to do this.
Any of the above with 'pretending to be' any of the above. Any of the above + any of the above. Half of any of the above with any other half (I have played, successfully, 'They are desperately trying to find a job'). Any of the above + half of any of the above with any other half.
The simplest is always the dreamer, leaving home to seek fortune, fame, riches, girls, success, powerful magicks, whatever. People leaving home to seek stuff isn't really common in this age of globalization, but most fantasy worlds aren't globalized - leaving Peasantville McFarmingland (or isolated forest land) behind with little to no idea where you were going or what you were going to do was the only way to advance oneself in any way - and odds were, you'd die horribly long before you even got close (just like adventuring!).
My favourite thing for that concept, though, is this;
Raised by Owlbears
Tarzan was raised by an ape, Mowgli was raised by a bear, Romulus was raised by a wolf, and in the D&D world your character can be raised by creatures much more exotic. The sky is really the limit here: simply pick some improbable beast and your character was protected and fed as a small child by that beast after she was orphaned or abandoned in the wilderness. While I'd like to think that we've all read enough Burroughs that this story pretty much tells itself, the truth is even more astonishing. This character background has become cliché and we're totally fine with that. You can really have an interesting and memorable character with a clichéd backstory and a three sentence intro that ends with "And then I came to this village to reclaim my birthright as a gnome."
Frank and K's Races of War