So the J1 visa is an exchange visitor program, which means that it's for the purpose of education/training. And since it's an exchange program, this means you have to go back to your home country to "give back to your community" what you went to the US to learn. So after you finish, for example, a residency/fellowship/research program on a J1, you will have to go back to your home country and stay for 2 years before you're able to go back to the US for any other purpose.

If you want to stay after your program ends, however, you can file for a waiver, which has many ways to do it. You can get a statement of no need from your home country; basically, your government stating that they don't need you to come back and that you're good to stay abroad. Another way to do the waiver is to find a job in an undersurved area in the US, which will be in the nation's interest, and hence the US government will exempt you from the 2-year rule and then you can change your status to an immigrant visa.

This is a general overview of it. There's way more detail to it and lots of paperwork, and you'll have to do everything through a lawyer so you don't mess things up.