Ellen White was a primary influence in the development of the SDA Church. She continued to be a leader in the church throughout her lifetime, and since she was also an author her influence has continued to the present day.
She was the author of the Great Controversy and other books.
I think EastCoastRemnant summed it up pretty well. SDAs tend to agree that her books and her influence can be very helpful, but they tend to differ on how strongly they hold to her advice. October of 1844 was an event that Adventists call The Great Disappointment. It was a time when the Advent Movement was in its infancy and lots of people believed very strongly that Jesus was coming back and they were very excited for that to happen. They predicted that it would happen in October 1844, and when it didn't they were very disappointed. As to what actually did happen in 1844, there's a variety of theories and Adventists don't all agree. But we tend to agree that something important happened, even if we may not agree on what that was.

If you're interested in Advent history, a good resource is author George Knight. He has several short books on Adventist history and I think he does a good job of being objective and fair. I would suggest
A Brief History of Seventh-day Adventists and/or
Meeting Ellen White.
As far as their being essential beliefs to join an SDA Church.... I think you're thinking of our beliefs in a different way than we intend them. The 28 Fundamental Beliefs of Seventh-day Adventists are not a creed one must adhere to in order to join the Adventist church. They are a statement of what we tend to agree upon, as a way to be clear in our teachings for the benefit of new converts and evangelism and as a way to make sure we're all on the same page as a church community. You don't have to agree with every point in order to associate with us. And even if you do agree with the core beliefs, you don't have to agree with every way they are taught by every person. There's room for a lot of diversity within our community. Personally, I really appreciate that about our church family.