This is another one of those expressions which became popular thanks to Aesop's fables. According to the story, a young man sees a swallow on a warm winter day. Since swallows are usually seen only during spring, the young man thinks that spring has arrived. As a result he sells his winter coat and then proceeds to drink with the money he has made. A few days later, it becomes extremely cold again and the young man shivering in the cold realises that one swallow does not necessarily imply that summer has arrived. Other expressions which have more or less the same meaning are "one grain does not fill a sack" and "one actor cannot make a play
It also tells you to pay close attention to conversations – are you saying more than you should? Are you listening closely to what others have to say? Swallow also brings a warning to not let small things get to you – don’t let the mundane activities of life take up all you time and prevent you from moving forward. Rise above the small stuff and you will gain a better perspective on your life. The key is objectivity.