Sometimes if you do a search, you will have to enter a code in the box to prove you're a real person and not a bot doing searches. That's the only time I've ever had to "claim" swagbucks. One time I did a search for something while I was at work, got involved in something else, and forgot I did the search. When I came back to the window and saw that I had won swagbucks for my search but I needed to enter the code, I tried to enter it, but it had timed out, so I lost the swagbucks I'd won in that search.
I'm pretty sure that's what it means by claiming them because that's the only time I've ever had to do anything to claim them.
Your toolbar also doesn't automatically update which is probably why there's a discrepancy between what your account page says and what the toolbar says!