Esse is the first singular form of the verb "essen" (= to eat). Ich esse = I eat

I don't think that there's a word "esst" in German. Do you mean "isst"? :-)

Esse > Ich esse Käse = I eat cheese

Isst > Er isst Käse = He eats cheese

They are different conjugations of the same verb.

essen (to eat):
ich esse (I eat)
du isst (you[sing. inf.] eat)
er/sie/es isst (he/she/it eats)
wir essen (we eat)
ihr esst (you[pl. inf.] eat)
sie essen (you[pl. form.]/you[sing. form.]/they eat)
sing. = singular, pl. = plural, inf. = informal, form. = formal.