To "apply" makeup means to put it on someone (yourself or someone else).
The word "apply" sounds technical, so you would use it in situations like when you're giving someone instructions. An employee at a department store might use "apply" when talking about cosmetics in order to sound professional.
In normal speech, use "put on" instead of "apply":
First I'm putting some eyeshadow on you.
You can also "apply" things other than makeup: