It's a pub staffed by Filipina hostesses. All offer drinks and conversation, most do karaoke (Filipinos love their karaoke!), some have dancing and shows. The term itself doesn't connotate sexual services, although the virtue of some ladies may well be negotiable after-hours.
The phenomenon started when the bursting of Japan's economic bubble led to a steep fall in Japanese visitors to the Philippines, leading many of the people in the industry that had developed there to try their luck in Japan instead. The Philippine pub boom reached its peak in 2004, when there were over 80,000 Filipino women in Japan on "entertainer" visas.
Shortly thereafter, Japan landed on a human trafficking watchlist and started cracking down heavily on these visas, so much that by 2007 they became effectively impossible to obtain. Some pubs scraped by through finding staff who were either married to Japanese (for real or otherwise), had legal working status via some other means, abusing tourist visas or simply overstaying illegally, but obviously this put a big crimp on the industry and there aren't that many left.
(Most of the above freely translated from フィリピンパブ on the Japanese Wikipedia.)
And yes, foreigners are generally welcome, probably more so than at your average Japanese bar since most Filipinas speak decent English. But I suspect I'm not entirely alone in not really understanding the attraction of paying fairly sizable amounts of money to drink with people who are employed to pretend to like me...
