Why scientists care
An ion is an atom or molecular entity carrying a net electric charge because its numbers of protons and electrons are not balanced.
Losing electrons gives a positive charge; gaining electrons gives a negative charge. This simple bookkeeping is behind salts, electrochemistry and much of solution chemistry.
A concrete example
Na loses one electron to form Na+; Cl gains one to form Cl−, while their proton counts stay unchanged.
Try to notice
Science becomes memorable when a definition is connected to something measurable or observable.