Translation:My brother likes both eating and cooking.
This construction is very similar to French: "Il aime et manger, et cuisiner". You can of course say "Il aime manger et cuisiner", but it often finds its uses when the two things you want to join are slightly opposite but still present. You want the non mutual-exclusion to shine.
In our example, he likes both "eating" and "cooking". One action consumes meals, the other produces them .. And yet, he likes to do both.
The verb to eat = Есть
Conjugated thus: I eat = я ем you eat = ты ешь he/she eats = он/она ест (the wolf would be he in this case, yes without the ь) It is confusing having the у меня есть construct, the есть in this case having nothing to do with the infinitive of the verb to eat (есть), but that's Russian for you. English can be confusing too, I saw a sign in a field for 'May's Maize Maze' May being the owner of the farm, Maize being what was growing in the field and Maze being what they had made in the field out of the Maize! And all pronounced the same.
есть is the infinitive 'to eat'. Without the ь (ест) it is the third person singular of есть. Он ест хлеб for example. If you wanted to cojugate the english verb 'to eat', it would be: I eat, he eats, she eats, we eat, you eat, they eat. In Russian to conjugate есть: Я ем, ты ешь, он ест, and so on.
есть also is used to denote existence. У меня есть -- I have
Just as above in Russian, in English we sometimes use the same word for different things. Lead (pronounced leed) is both a verb "Lead him to water" and a noun "I have the dog on a lead" (leash) -- as well as other things, like "the lead in the play".
Pronouced differently, Lead (pronounced led) is the metal that bullets are/were made from.
Similarly, duck is both a verb (bend low so something misses you) and an bird.