A Capitalist economic system is one characterised by free markets and the absence of government intervention in the economy.
In practice a capitalist economy will need some government intervention, primarily to protect private property. (this is important to distinguish capitalism from anarchism, where there is absolutely no government present)
In the real world, many economies which are viewed to have a capitalist economic system may have government spending taking up 35% of GDP. This is because the government pays for welfare, health, education and national defence. However, the economy is still viewed as capitalist because in the area of private enterprise, firms are free to decided what to produce and for whom.