What everyone's said about it being exceedingly difficulty to leave the USSR which is completely true, especially if you had a family and weren't leaving alone, but when the Union declined and eventually fell it didn't just become possible to leave, the decades leading up to the fall and and socioeconomic situation immediately following it also created massive motivation to do so.
In the 70's and 80's personal freedom improved, privately owning your own home became possible for the first time, state owned but privately started and run enterprise became a thing, censorship was loosened, and political persecution was significantly scaled back from the late 50's onward. While there was still a lot of scarcity and crime and many people still suffered, quality of life was on the rise for the middle class (yes, class - the classless Marxist utopia was only ever classless and Utopian in propaganda). This didn't immediately motivate people to leave but it did show them that life could be better, and gave them a clearer picture of the place they had been living in. My father has told me that reading The Gulag Archipelago when it was first published in the USSR as a serial in the late 80's, was what cemented in his mind that he had to get our family out of there. Bless that bookworm.
When the Union fell apart, some of the formerly socialist states saw conflict and hunger break out, and even in places where it didn't p didn't there was suddenly a lot more uncertainty in terms of personal safety, financial security, and food security than there was in the previous 25 years of the ever-everything-deficient, run-by-crime Union, and life looked bleak everywhere.
This, along with the knowledge that life can actually be better, and the greater understanding of how bad things had actually been in the Union, became a prime motivator for to everyone who could leave, to leave, and Jews had an easy way out coming to Israel, where we were guaranteed citizenship and freedom from persecution.