My definition of success, is someone who has achieved something that is important to them. Or someone who has, against the odds, made a good life for themselves.
For example, I hate to use myself, but I dropped out of school when I was 16, I had no grades, nothing. I somehow blagged my way into college, and was kicked out a few months later. 10 years down the line, I work for a bank, on quite a tidy wage. To me, this is success.
Another example: A man takes a risk, invests his only £1000 into a small business, 5 years later, he's a millionaire. This is success.
What success is not: Being handed everything on a plate.