Definition 1

When used as an adjective, illegal refers to something that is not legal or lawful. Most often it refers to behavior. For example, murder is recognized as an illegal act throughout the world.

Definition 2

Behavior can be determined to be "illegal" aside from matters of law by being simply against official rules or regulations. The term is used quite often in sports in regards to rule-breaking. For example, "illegal touching of the ball" in American football is when a pass is made to an individual other than those predetermined as eligible to receive it.

Definition 3

In regards to computers, "illegal" can refer to any action that is unacceptable or not performable on a computer. An illegal operation can be an attempt to close a program which the computer relies on for basic functions.

Definition 4

Illegal is often used in the form of a special combination, as in illegal alien, illegal immigrant, illegal operation or illegal seizure of property or an illegal block (in football). Often, the addition of "illegal" to a phrase carries negative social connotations as well.

Social Connotations

In some societies and at certain times in history, the term "illegal operation" would refer to an abortion. The terms "illegal aliens" or "illegal immigrants" are at times truncated to "illegals" which can be interpreted as a derogatory or an otherwise negative term.

Source:

Dictionary.com

Oxford English Dictionary