This denotes how many generations to a common ancester
and how many generations difference.
Example: On your mothers side. She has a sister and this makes her your aunt. She has a daughter and that daughter has a daughter. The first daughter is your first cousin, the second daughter is you second cousin.
Now for the Removed Part: Again on your mothers side. Her GGG Grandfather was your GGGG Grandfather. He had a brother, that brother is you GGGG Uncle, and he had a son. That son, is your first cousin 4 times removed. Because you had to go back 4 generations to connect to a common ancester.