A dichotomous variable is a member of a group which can only belong to one of two categories within the group.
It is a type of categorical variable, categories divide things into sets. A dichotomy divides some sort of group/set into two jointly exhaustive and mutually exclusive sets (it must be one or the other option and can not be both.)
Example of a dichotomy: you are either dead or not dead (this is otherwise known as alive)
Also goes by the name of dummy variable or indicator variable