This is how I understand the meaning of about 1st, 2nd cousin...

you and your 1st cousin have the same grandparents, i.e., one of your parents and one of your 1st cousin's parents are brothers/sisters;

you and your 2nd cousin have the same great grandparents, i.e., one of your grandparents and one of your 2nd cousin's grandparents are brothers/sisters;