A fomite is any object that can facilitate horizontal bacteria transmission of bacteria or virus (person to person). Almost every object on earth could theoretically act as a fomite.
A good example would be a doorknob:
Someone with an infection (that has the infection-causing bacteria on their hands) touches a doorknob, then you touch that doorknob and then touch your nose or mouth, then you get the infection. The doorknob acted as a fomite, and you just got a fomite borne infection.
Another example would be food:
Someone with an infection sneezes on your food (or near your food), then you eat that food, then you get the infection. The food acted as a fomite, and you just got a fomite borne infection....