It implies a level of interest. Under conditions of high involvement, or high self-relevance, the individual will tend to process information objectively, or rationally, via what is called the central route. Under conditions of low involvement, processing will tend to be more subjective and emotional, via what is called the peripheral route. When the central route is employed there is a higher level of logic than when the peripheral route is employed. Along the peripheral route the individual is more subject to affect than cognition.
High involvement implies a greater attention to what is being said than to how it is being said.
Low involvement implies the reverse. This is an important distinction because attention is being paid in each case. Many newcomers to the study of involvement make the mistake of equating low involvement with a lack of attention. It is more a question of what is receiving the attention. Human beings are almost always paying attention to something.