In general statistics mutual exclusivity describes a scenario in which the occurrence of one situation or event doesn't affect or influence another situation or event. To be mutually exclusive these situations also cannot happen or exist at the same time with one precluding the other from happening.
A simple example is a coin toss- 'heads' and 'tails' are mutually exclusive results to a coin toss. If the toss lands on 'heads' then it cannot land on 'tails' and 'heads' and 'tails' cannot happen at the same time.
Another example of mutual exclusivity would be choosing a red or black card from a deck of cards. Red and black are mutually exclusive in a deck of cards- choosing a black card makes the choice of a red card impossible. It is an either/or situation, it cannot be both at the same time. In developmental psychology mutual exclusivity describes a situation in early language acquisition in that that only one name or label can be applied to an object. This limits the abilities of very young children to fully comprehend how naming and language work. Mutual exclusivity can influence a child's language acquisition in a few ways.
For example, the disambiguation effect results from mutual exclusivity. The disambiguation effect can be seen when a child is in the presence of an unfamiliar object (a toy rhino) along with a familiar object (a toy dog). When given a new word they haven't learned ("pooky") and asked to pick out which object is a "pooky" they will attach the novel word to the rhino without knowing exactly what it is. This suggests mutual exclusivity: they know that the toy dog is a "dog" and since it cannot be anything else then the rhino must be a "pooky." Children don't understand that things can have different names and still be the same thing (dog, pet, animal, mammal).