I picked it up from TVTropes, who picked it up in turn from the fandom of Stargate Atlantis, where it was used to describe a character - Rodney McKay - who pretty much epitomized the term (oooo - there's another one - epitome - but I digress). It's used to describe a person who is dorky, geeky, or nerdy in some way that makes them endearing. The characters (and real life people) who particularly fit the definition tend to be scary-smart (or otherwise powerful) and they may or may not have social skills (or may have them but forget to use them), but are good people. They tend to squee over things that interest them. They're not the stereotypical super-smart jerk.
- The titular Monk is adorkable but Dr. House is not.
- Peter Parker is adorkable.
- The titular Wall-E.
- Marty McFly. Mentor Doc Brown has his moments, but he's more of an Absent Minded Professor / Mad Scientist than adorkable.
- Daniel Jackson from Stargate SG-1, along with the aforementioned Rodney McKay.
- Several Doctors of Doctor Who (especially Ten, but even Nine had his moments).
- Willow and Xander from Buffy the Vampire Slayer and Wesley in earlier seasons of Angel.
- The title character of Chuck.
- Niles Crane of Frasier.
- Sam Beckett from Quantum Leap.
- Luna Lovegood and Neville Longbottom of the Harry Potter stories.
- Vivi from Final Fantasy IX.
- Phineas, Ferb, and their dad Lawrence.
Many of the males I consider to be friends also qualify (see link above). I met my husband online and thought, "aww, how sweet" when I saw his tagline (Nerdy and Good at It). Uh... I just realized. I may be adorkable myself. Just a little.