A lawsuit is a civil legal action brought in a court. Typically one "party" is suing another party for money or other property. (The term "party" can include individuals, businesses and government agencies.)
The person suing is typically called the "plaintiff"; the person being sued is the "defendant".
Lawsuits sometimes also involve an action to "enjoin" (a legal term than means "restrain" or "stop" ) a party from doing something, such as picketing or trespassing on your property or disclosing confidential information.
A lawsuit is one way that people and companies can resolve disputes arising out of an infinite variety of factual circumstances.