You start with the number 'a'.
Somebody comes along carrying the number 'b', and you say to yourself
"Hmmm. I wonder if I could take his number 'b' and somehow make my
number 'a' just that much bigger ?"
Suddenly, the light bulb over your head lights up, and you know how to do it !
You'll use addition.
You take his number 'b' and add it to your number 'a'. Your number immediately
gets bigger. The amount bigger it gets is 'b'. We say that 'a' has increased by
the amount of 'b', or simply increased by 'b'.