Experimental philosophy studies people's intuitions about philosophical questions. It has nothing to do with anthropology. In many philosophical debates philosophers appeal to intuition, and especially intuitions about certain thought experiments. For instance, there is the famous Gettier problem, according to which knowledge isn't justified true belief. Here's an example of such a Gettier case: X sees a clock that reads 3 o'clock, and on that basis X believes it's 3 o'clock. It is indeed 3 o'clock but, the clock is in fact defective -- it just stopped at 3 exactly 24 hours earlier. Intuitively, X doesn't know that it's 3 o'clock, even though X has a justified true belief that it's 3 o'clock.
The appeal to intuition here is important: it seems to us that there is no knowledge in the Gettier case above, but this judgment in not based on any theory, it's just a matter of intuition. But whose intuition is it? Is it supposed to be everyone's intuition? What if some people have different intuitions?
Here is where experimental philosophy comes in. There have been studies specifically on Gettier cases such as the one above. Initially, it was found that people's intuitions about Gettier cases differ across cultures (Weinberg et al. 2001): in some (eastern) cultures people thought there was knowledge in Gettier cases, and in others (western) people thought the opposite. If these results are reliable, then perhaps Gettier cases don't provide counterexamples to the justified-true-belief theory of knowledge after all. In the SEP entry on experimental philosophy it is put this way:
This apparent diversity in intuitions about philosophical matters has been used to challenge the use of intuitions in philosophy to tell us about the nature of things like knowledge and reference. If intuitions about knowledge turn out to exhibit diversity between populations, then this looks to put pressure on a traditional philosophical project.
However, more recent studies did not find variance across cultures (e.g. Machery et al. 2015), and this seems to confirm Gettier counterexamples.
All this is to illustrate that experimental philosophy takes an experimental approach to traditional philosophical questions, and specifically to those intuitions that philosophers appeal to in their arguments and thought experiments.
Weinberg, Jonathan M., Shaun Nichols, & Stephen Stich, 2001, “Normativity and Epistemic Intuitions”, Philosophical Topics, 29(1/2): 429–460
Machery, Edouard, Stephen Stich, David Rose, Amita Chatterjee, Kaori Karasawa, Noel Struchiner, Smita Sirker, Naoki Usui, & Takaaki Hashimoto, 2015, “Gettier Across Cultures”, Noûs, 51(3): 645–664. doi:10.1111/nous.12110