The song is based on Timon and Pumbaa's common catchphrase in the movie, Hakuna matata, which is a Swahili phrase. The two main comedy characters in the film, (Timon and Pumbaa), talking about moving on from their troubled past and forgetting their worries. The song also provides a back story for Pumbaa, explaining that he was ostracized from animal society for his excessive flatulence.
Hakuna matata is a Swahili phrase that is frequently translated as "no worries". In bonus features of The Lion King Special Edition DVD, the film's production team claims that it picked up the term from a tour guide while on safari in Tanzania. It was then developed into an ideology that, along with the seemingly antithetical value of duty to the monarchy, is central to the moral content of the film.
To me this song and its lyrics are so important. Life is stressful and chaotic and so much happens that we never just stop and take time out to have fun. People always stress and are always worried about life and this song and the meaning of Hakuna Matata is to just forget everything and not to worry as much as we usually would. Sometimes in life there are situations where people need to think of Hakuna Matata