A zombie's energy level can be found as a red strip at its interface when clicked, and is very important. It lowers when the zombie is doing work (cooking or serving), and if it gets too low the zombie will start attacking the customers, which will scare them away and isn't going to be good for your cafe's rating. Also, the lower the energy level , the higher the chances are of the zombie daydreaming (although it still does happen at high energy levels but not so often). It is replenished by resting, so you should always have some of your zombies resting. It is also gained by eating customers (both on raids or at home) and enemy chefs, although this is hardly effective.
On a raid, a zombie's health is accounted for by its energy level. It is thus a good idea to close your cafe and have all your zombies rest for a while before a raid for maximum effect. If a zombie loses all of its health on a raid, it will have to reanimate for 8 hours before it can do any work again, and after the 8 hours it will only have about a quarter of the full energy level.
Some different types of customers have energy level related attributes once infected. For example, teenagers (and all the upgrades) have a faster energy loss rate, but a much faster replenishment rate than normal. Construction workers along with their upgrades are the opposite - slow replenishment, but equally slow loss.