"Anne boit une bière et tu bois un café."
Translation:Anne is drinking a beer and you are drinking a coffee.
"Bois" is used in instances of the first person or the second person, i.e. "je bois" and "tu bois." "Boit" is used with the third person, i.e. "elle/il boit" or "Anne boit." Think of it as the French equivalent to how we say "I drink" or "you drink" but "she/he drinks" (with an 's') in English.
Note that "bois" and "boit" are referred to as verb conjugations of the infinitive verb "boire," which means "to drink." Conjugations tell us which forms of a verb to use with a particular pronoun, as demonstrated above. Hope this helps!