A fomite is an inanimate object which is capable of transmitting an infectious disease or organism from one person to another. In this it is similar to the medical concept of a vector, which is an organism which has such an ability.
An obvious example of a fomite is a comb on which head lice have made their temporary residence. Dirty surfaces, towels, or even improperly disinfected medical equipment can act as fomites for many kinds of diseases.
Contaminated dust particles and saliva droplets which are thrown into the air by a sneeze are a kind of fomite.