Hi there! First lets discuss what's" first order". I'll just pull the definition of the first order reaction here: "A first-order reaction is a reaction that proceeds at a rate that depends linearly on only one reactant concentration."
So this tells us that in radioactive decay, there is a linear relationship for the rate of decay and the amount of substance.
Now it follows first order kinetics because each individual radioactive atom has an equal probability of decaying at any given time.