Answer:
A Second Cousin is related to you by having the same great grandparent that you have. Your second cousin is the child of your parent's (first) cousin. "Second cousin" mean two generations below the sibling relationship. So, third cousins would be the relationship between the children of second cousins.
Your parent's cousin would be your 1st cousin once removed. "Once removed" means moved away from the relationship by one generation. Your parent's cousin would be a 1st cousin twice removed to your child. Interesting note, cousins "removed" usually is a relationship term used only when referring to the upward generational relationship. In other words, while I might call my mom's cousin "my cousin once removed", my mom's cousin would likely refer to me as "my cousin's child."