To understand this phrase, imagine a little dog which has been trained to do circus tricks. In order to get its food, it has to jump through several hoops or rings: one big one, one small one, some very high up, and maybe one that's been set on fire.
When people make you do a lot of unnecessary work, you can say that they're "making you jump through hoops". For example, when you're applying for a green card you have to:
- Fill out an application
- Sign the application in front of a licensed "notary public" who confirms that you signed it
- Make copies of your documents like your passport, marriage license, etc.
- Get a medical checkup and vaccinations
- Get confirmation that you have no police record
- Get all documents translated into English
- Have an interview
These steps are complicated and annoying, so you can call it "jumping through hoops."
Another example is when you try to cancel your telephone bill. The telephone company doesn't want you to quit easily, so they make you "jump through hoops."
all kinds of (something)
"All kinds of ___" means "a lot of ___" or "many different kinds of ___". In the example above, it means that people who want to immigrate to the U.S. have to do a lot of work to become a permanent resident.