A "bitch" is literally a female dog, but it is used as a slang word to describe a disagreeable female or even a disagreeable situation. The meaning can change depending upon the tone of voice used and the context.
Someone might disappoint you in a proposed business deal, and you might utter: "That son of a bitch promised me he'd sign the contract today!" You're using the term in an angry context in this case.
Or you might be pleasantly surprised that your horse won an important race: "I never thought the son of a bitch could do it!" It's still considered to be profanity, but in this case you're not addressing anyone in anger; you are using it as a phrase to express incredulty.
Some folks might exclaim "Son of a bitch!!" in pain and anger when they hit their thumb with a hammer by mistake, or stub their toe.
Overall, however, "son of a bitch" is usually considered inappropriate for polite conversation, and is usually only used in extreme frustration or among close co-workers or friends.