A casual gamer is someone who shows a casual interest in gaming. They can also be known as non core (non hardcore) gamers as well. Casual gamers are hard to define as so many different types of games can fit into this niche.
A gamer who only plays The Sims and nothing else can be known as a casual gamer. They casually play one game and whilst they may be very into The Sims playing it for hours at a time they may show little to no interest in other games. In fact they may not even see a game such as The Sims as a game, instead just something to do or that they like.
A gamer who plays Maddern and Modern Warfare 3 may be called a casual gamer. Whilst they play different games and have a small collection they will stay with safe bets, the big hitters and only play them each year. They won’t check out games like Shadows of the Damned or Super Mario 3D Land because they see those as hardcore games of kiddy. They play Maddern, they play Modern warfare until the next year when the new releases come out.
Even someone who owns lots of consoles and buys lots of games can be a casual gamer. They may love video games but never have the time to play them. Instead grabbing 20 minutes to play Angry Birds on the train and then spend 30 minutes at home slowly working their way through Skyrim. If they had the time and money they could easily become a hardcore gamer but life gets in the way. They put going out with friends over playing video games and more often than not have a family.
So a casual gamer can pretty much anyone, but check here if you want to see what a hardcore gamer is.