boire = to drink (infinitive) while boit = drinks.
"Il aime boire du vin" = "He likes TO drink wine"
while "Il aime boit du vin" = "He likes drinks wine"
You only conjugate the first verb, and the following ones are left as the infinitive.
In English it's "I like to drink to forget". The verbs after like are in the infinitive form "to x".