What Wikipedia says...

Cosplay (コスプレ kosupure?), short for "costume play",  is a type of performance art in which participants don costumes and accessories to represent a specific character or idea. Characters are often drawn from popular fiction in Japan. Favorite sources include manga, anime, tokusatsu, comic books, graphic novels, video games, hentai and fantasy movies. Role play includes portrayals of J-pop and J-rock stars, Taiwanese puppet characters, science fiction characters, characters from musical stories, classic novels, and entertainment software. Any entity from the real or virtual world that lends itself to dramatic interpretation may be taken up as a subject. Inanimate objects are given anthropomorphic forms and it is not unusual to see genders switched, with women playing male roles and vice versa.

Cosplayers often interact to create a subculture centered around role play. A broader use of the term cosplay applies it to any costumed role play in venues apart from the stage, regardless of the cultural context.

What the Cosplayers from Nema say...

EDMUND HEWITT: "Cosplay" meaning costume play. it is the act of dressing up as your fave anime or manga character. stepping to your fave characters shoes so to speak.

(One of my favourites) SERENITY:
Cosplay to people is almost an escape from reality.
A chance to pretend to be someone else for a day, and getting rid of societies lables.^^
Its about having fun and making friends, and at the end of the day, its nothing more than a good chance to dress up :D

CATT RYUK-RAWR (Her FB name): 
Cosplay is when people can dress up as someone they admire/like, (:

And finally, XD says: It's a really fun way to get talking about your favourite manga/anime, to people you're not familiar with. It's great when someone compliments your outfit too :]

And in both videos Trick Tester (yours truly) is the one in the Red and Black Tights and black skirt!