An independent variable, a term used in math and statistics, is a variable you can manipulate, but it's not dependent on the changes in other variables. The independent variable is usually indicated by "x" and the "dependent variable" is "y."
Say you have two puppies, both from the same litter, and you want to see if it matters what dog food you feed them. You feed Butch organic Mighty Pooch, and you feed Slim Frooty Loops for Dogs. The independent variable is the dog food, the variable you are changing. The dependent variables are the possible results you observe — the dogs' weight gain, the glossiness of their coats, and whatever else you think might be a result of the dog food.