What is mentioned in the responses is mainly using the word when facing an option. However, what I am trying to also convey is that we tend to take the easy way out by using this word when we just don't wish to take a firm stand or to avoid conflict. Suppose there is a quarrel that is needlessly getting stretched with back and forth views, we may suddenly get fed up and say "Whatever!" just to end the quarrel. We may even use it when we don't want to take sides when asked for an opinion on somebody's suggestion at a meeting. Just so we don't want to offend the boss or our colleague, we may shrug our shoulders and say "Whatever", implying that we are ok with whatever the decisions will be. That way, if the suggestion does not work out well, we feel that we are safe from receiving any backlash.
When you make a commitment, you create hope. When you keep a commitment you create trust! ~ John C. Maxwell