From wikipedia:

Attention is the cognitive process of selectively concentrating on one thing while ignoring other things. Examples include listening carefully to what someone is saying while ignoring other conversations in the room (e.g. the cocktail party problem, Cherry, 1953). Attention can also be split, as when a person drives a car, puts on makeup, and talks on a cell phone at the same time. (Never really try this, however.)

Attention is one of the most intensely studied topics within psychology and cognitive neuroscience. Of the many cognitive processes associated with the human mind (decision-making, memory, emotion, etc), attention is considered the most concrete because it is tied so closely to perception. As such, it is a gateway to the rest of cognition.

The most famous definition of attention was provided by one of the first major psychologists, William James:

“Everyone knows what attention is. It is the taking possession by the mind in clear and vivid form, of one out of what seem several simultaneously possible objects or trains of thought…It implies withdrawal from some things in order to deal effectively with others.” (Principles of Psychology, 1890)