SERP stands for one of the following (depending upon who you ask):
1. Search engine results page
2. Search engine ranking page
3. Search engine results position
4. Search engine ranking position
When I refer to SERPS, I am speaking of the actual position within the search engine results. So if my keyword is ranked number 12, then my SERPS is 12. Some people use the PAGE number rather than the POSITION number, but I think the POSITION number is the most common.