You pay a higher price than regular admission and get a card that lets you visit that zoo for free any time within a year. At most zoos the annual membership is between two and three times the price of a single day admission. So if you visit a zoo three or more times within a year you are saving money.
In Detroit a family membership--two parents and up to four children--is $109.00. I don't know offhand if this is the price for residents of the three county area, who get some small discount because a millage goes in part to the zoo. At the gate prices are $18.00 for adults and $15.00 for children 2-18. So if the parents and two kids go more than once a year it pays to have a membership. And if you travel at all, as said above, a lot of zoos offer reciprocity, usually half off. Also, I think parking is another $6.00, and members don't pay for that.
I live quite close to the zoo and usually go once a month or so, so I more than make my money back.