Why do people leave Eretz Yisroel to go to Uman for Rosh Hashanah? (It seems to me like leaving America for July Fourth.) In general what is the reason people go: is it Just a festival in the Woodstock sense (as the Israeli Media seems to make it out to be)? Also, why is it that there are no women allowed? Finally, if it is religious, than why do so many irreligious people go there?
Breslever chasidim leave E"Y to be by our rebbe at Rosh Hashana because he said to come, end of story. Not all Breslevers go - one of the great leaders of Breslev today, R' Elazar Kenig shlita, hosts a gathering in Meron for those who are unable to go. There is no specific issur in Uman. The issues of kivrei tzadikim and leaving E"Y in general are complex and probably should be asked as separate questions.
It is more than a festival, even if some make it out to be that. Bli neder when I am at home I will add here some of what Reb Noson z'l writes about being in Uman for R"H. Rebbe Nachman zy'a himself felt that encouraging Jews to come to the burial places of the thousands of victims of the Chmielnitzky massacres was very important.
Women used to go at R"H, although never in great numbers. As the number of male attendees has increased, Breslev leaders have urged women not to come out of tznius concerns. There is a larger women's gathering at Purim. As for secular Israelis and even Jews who are not chasidim of Rebbe Nachman in general, see my comment to Gershon Gold's answer.
Those that go to Uman - go because they believe that Rabbi Nachman promised that if you come and pray at his grave on Rosh HaShana he will make sure that you have a good year. Many Rabanim are against this (Harav Ovadia Yosef amongst them). Woman do not go on Rosh HaShana both for Tznius and practical reasons (someone has to take care of the family). Regarding the irreligious that go there - I guess there must be some sort of spiritual pull that is calling them there.
The Rebbe did not state that anyone who comes to his grave and prays will be granted a good year. He made a promise that anyone who travels to his grave, recites the Tikkun K'lali, donates at least a couple pennies to charity in his name, and, perhaps most importantly, take it upon himeself to leave his errant and foolish ways, then the Rebbe will do everything he can to save this person, even travel through the fires of gehinnom and pull the out by their payess if needs be. As per traveling to Uman on Rosh Hashanah, the Rebbe said that "Rosh Hashanah is go rmein zach" Rosh Hashanah is my whole thing. In Chayei Moharan, Reb Nosson writes about one R"H near the end of the Rebbe's life, there was one chossid who desperately wanted to be with the Rebbe for R"H, but the Rebbe told him he had to go home. On R"H, the Rebbe explained to others there, that as painful as it was for this chossid not to be there, it was all the more painful for the Rebbe not to have him there.
It says very clearly in the zohar that there is no issur of speaking to a dead tzadik auviously it must be a real tzadik wich he undoubtedly was. if a breslover didnt go on rh that would be a lack of emuna in the words of the tremendous tzadik.
I'm not aware that the Rebbe really encouraged his followers to go to his kever on Rosh HaShanna. This custom probably began when Rebbe Nachman's chassidim started visiting Uman after his petira. They continued to go there for the same reasons that other Chassidim like to be by their Rebbes.
As stated by others, the Rebbe himself stated that he would go to the end of the earth and pull a person out of gehenom if they would travel to Uman, recite the Tikkun Klali by his kever, give Tzezaaka and do teshuva.