First, let's think of it from the perspective of a child. Your second cousin is quite simply the son or daughter of your Mom or Dad's cousin, which means that you share a great-grandparent with your second cousin. Confused yet?
Now think of it from the perspective of an adult. Imagine your cousin you grew up with. Now imagine your child and your cousin's child playing together...They are second cousins and share the same great-grandparents.
Cousin Once Removed
Now the key word here is "once removed," which refers to a generation below or above depending how you look at it.
From the perspective of a child, your cousin once removed is the cousin of your Mom or Dad. The terms cousin uncle/second uncle or cousin aunt/second aunt can be used. (which, by the way, sound kind of weird, right?)...Anyways...
From the perspective of an adult, your cousin once removed is the son or daughter of your cousin, who can also be called cousin nephew/second nephew or cousin niece/second niece.