stack

Exaple if you'r playing nasus when you kill minion with Q you got 3 stacks

 

Stacks can be not only skill's like nasus q it also can be items like mejai , rod of ages that gives you more mana ability power and stuffs like that for rod of ages u can only have 10 stacks max.
For mejai u can get 20 stacks max u can get them by killing champions or getting assists when u kill champ u get 2 stacks and per assist 1 stack for every stack u got more and more ap just then when u got 20 .
With nasus q when u kill minion u get 3 stacks and when u kill large minion u got 5 stacks with more stacks u got more damage on q ... and that's what stacks are

 

Stack is a certain amount of things u get. For example - extra dmg on Nasus Q, extra mana, ap and hp on Rod of Ages, Extra ap on Mejai's soulstealer.

 

Agree with guys up there.

Not every champion has stacks. Nasus, Veigar,... have stacks.
Items can also be stacked, but not all of them.

Be more specific.