Remember when you played dress-up as a kid? Yeah, that was fun, wasn't it? But you grew out of it, right? You put away your costumes and became an adult.
Cosplay is when you miss those last two steps and continue to play dress-up well into adulthood. Usually, this involves making and wearing a costume based on a TV show you like, or if you're even more of a nerd, a comic or a book.
Tumblr fans are especially fond of cosplay because they are obnoxious little shits that want everyone to see just how much they love Doctor Who, despite thinking David Tennant is the second actor to play the Doctor.