err it kinda hard to explain but il give it a shot!
You say 'I have a lot riding on something/someone' if you put all your expectations into that thing/person, and kinda take a risk with it/them.
So say I ask 'Mrs X' to do me a favour for something REALLY important, I would say 'I have a lot riding on Mrs X'!
Or if I decide I decide to quit school and start a buisness, I would say 'I have a lot riding on this buisness', as if it goes bad, then il be in a bad situation. And I took a risk (quit school) to start it.
So 'everyone has a lot riding on this' means everyone has put all their hopes into whatever 'this' means.
Hope i havnt confused you even more!!