Membership usually gives you access to exclusive events, days where you can get in before the zoo opens, free parking, discounts on food and in shops, access to members-only lounges in the zoo, things like that, as well.
Along with the zoo you join, in the USA the AZA has a reciprocity program that gets you discounts into many other AZA institutions if you're a member of one in the program.
https://www.aza.org/assets/2332/reciprocitychart.pdf Not all AZA places are part of it - most aquariums aren't, as well as many of the private (no government funding) zoos, like San Diego and Bronx - but plenty are.
So for example: Philly individual membership is $90. Membership gets me in free plus one guest, along with free parking, and 10% off on food and in the gift shops (plus the other stuff mentioned above).
As non-members, one visit for myself and a friend is $50 in tickets ($25 each) and $16 in parking. That's $66. Spending just $24 more for membership means the next time I visit, I'm already not spending anything on parking and getting one free entry. Any other visits that year cost me nothing, plus I save money on nearby (and not so nearby) zoos and get discounts in gift shops and on food.
This year I joined Elmwood Park, where membership is nearly the same as Philly but regular admission is cheaper and parking is free, so it would take more visits to make up the cost. But because I go to other zoos, I've already made up for the cost - 50% off at Philly, 50% off at Dallas and a discount in the gift shop, 50% off at Henry Doorly, 50% off for myself and a guest at Maryland in Baltimore, 25% off in the gift shop at Salisbury (free admission), etc.