There are a variety of reasons why a person would sigh a lot, but the act is generally a sign of being in a bad mood for one reason or another. It can indicate discontent, disappointment, frustration, defeat and a variety of other negative emotions.
A person who sighs a lot may be doing so as a way to regulate their breathing when they're feeling stressed. It may also be used as a cry for help or as a way to convey to other people that they're upset about something. Sighing a lot could also be a way for a person to get a mental rest, giving them a chance to regroup and get emotions under control.