About 40,000 go each year. Rebbe Nachman taught his followers it was very important to visit his grave on Rosh HaShana. Some Breslov chassidim go every year, while others might go once in a lifetime.
The most distinctive teachings of Breslov chassidus are the importance to praying to Hashem in one’s own words (hitbodedut) and going to Uman. (There’s a lot more, too, including a special emphasis on studying the Shulchan Aruch each day, “it is a great mitzvah to be happy always,” etc.)
Many BTs are attracted to Breslov teachings, and so many people (especially Israelis) who are on the path to becoming frum go to Uman, and it can be an important spiritual experience for them, which encourages them. There are also many frum non-Breslovers who go–Chabad, dati leumi, Yeshivish, etc.–because they have some interest in Breslov chassidus.