What does the property additive identity, additive inverse, multiplicative identity, and multiplicative inverse mean?

Additive identity is any number you can add plus zero. (So any number.)
Multiplicative Identity is any number multiplied by one.
Additive inverse is subtracting the positive number in an equation on both sides of the equal sign. 
Here's an example since that was a bad explanation:
x+3=15
The next step is to do the inverse of adding three to both sides of the equal sign so you're subtracting three.
and multiplicative is pretty much the same besides instead of subtracting you're dividing. I hope that helped! :)