The executive is the power or body, who executes and enforces the law. It has the authority and responsibility over the government. In most countries with a separation of powers, the executive is one of the three powers. The other two are the legislature and judiciary. This system is invented by the Frenchman Montesquieu and is today enforced in almost every democracy.
In most countries, the executive exists of a head of state, a head of government and several ministers. They enforce the law and are overseen by the legislature (the parliament). The executive doesn't interpret or judge the law. It can arrest criminals, but can't convict them. The judiciary convicts the criminals.