Cosplay pretty much translates to "Costume and play". You are playing around with the costume eg back in the days of the glory fancy dress when at every Halloween, people would dance the night away in night clubs in costume be it nurse, doctor, policewoman, or Countess Dracula. These people would perhaps act in character and act like their costume would expect them to act.
Nowadays even in Japan where the culture of cosplay became really popular and spread around the world, some people would consider wearing an office lady uniform, policewoman, nurse any work uniform as cosplay, as they are cafes around Tokyo where they are themed cosplay cafes, where waitresses would dress in a specific costume and play the character of the costume. This is seen in the popular maid cafes around Akihabara.
People may argue that cosplay is a "fad", it may look silly, odd and it is just fancy dress. Yes back when cosplay was new it was seen as fancy dress. I will always remember my first expereince cosplaying at a convention at TomoDaichi back in 2006. I was expecting fancy dress material and I was very unaware of cosplayers on the internet, so I was really taken with surprise being at TomoDaichi and seeing amazing costumes which have been hand crafted by the cosplayers themselves. Over time cosplay has gotten very popular and you can really see cosplay has come a long way since fancy dress.
You can say that cosplay has evolved from fancy dress relating to the start of this article, or cosplay takes fancy dress to a whole new world and level. Cosplayers that are really into this hobby spend lots of time and money on their cosplays. It is the quality of the cosplay that is very important. If you look at well known cosplayers like Ya ya han, Alodia, Yuki le Fay who become a costume designer through cosplay, you will see that none of them would wear tacky wigs you would buy in a costume shop and their costumes are crafted very well. Now I am not saying all cosplayers have to have the best material, many people prefer just to keep cosplay as a fun subculture where they can hang out with their friends in cosplay and have a laugh and they is nothing wrong with that. :)
Ya Ya Han her website - http://yayahan.com/
Alodia Gosiengfiao - http://blackmage9.deviantart.com/
Yuki Le Fay - http://www.yukicosplay.com/site/yuki/pt/home
Cosplay itself is a very vague term and many people have their own interpretation of it. Alodia pretty much explains cosplay really well in these quotes;
It's not just dressing-up, cosplay incorporates craft, sewing, make-up, wig and hair styling, photography, acting and more. "And most of all, cosplay crosses geographical barriers.
Well to me and to many people that is what I describe cosplay as. Cosplay is like impersonating, you are impersonating a fictional character rather then a real person. You learn the mannerisms of that character and role play as that character. The character can be from a Japanese animation, manga comic, video game and any Western comic, graphic novel.
People have a misunderstanding that because cosplay is from Japan it is only called cosplay when the person is cosplaying as a Japanese character this is not true. There has been debate on which country actually started cosplay. Back in the 1970s when there was major hype with the Starwars and Star Trek movies people would cosplay as Star Wars/Star Trek characters to Sci-Fi conventions so it can be said that cosplay actually began in nerd culture from Sci-Fi conventions not anime conventions. In the photos below here are examples of sci-fi cosplay from the 1970s.
These photos were taken from this blog, if you are interested in seeing more. It is fascinating to see that cosplay goes back a very long way so there is no way it can be a fad.
However it has also been argued that cosplay in Japan began to get popular at this time period with people starting to cosplay as anime and manga characters and movies at douijin (fan made comics) events like the most well know one Comiket Market.
Comiket market and cosplayers
I originally had the Culture of Cosplay in this entry but it was way too long so I had to split it.