This is a traditional English folk song that has been around for a long time, and it has even been mentioned by Charles Dickens before. Someone who is hoping to learn more about the nursery rhymes of old should remember that this one is a simple rhyme that is really about tea, but Polly Put The Kettle On has made it so that you can learn some English history at the same time. Someone who is making tea would sing this to their kids, and then their kids would sing it on their own.
There are other variants of names used in this rhyme that are interesting because we do not use them anymore, which offers opportunities for you to research with your children. Which, apart from actually singing the song or reciting the rhyme together is a great way to promote literacy. It also offers an opportunity to get creative and change around the song lyrics to use names of kids in your family or circle of friends. They will be happy to sing this song just because they want to know that they are a part of it, and you can teach it to the kids pretty easily.
The song itself has a melody that dates way back, and that means that it is already out there where a lot of people are going to know it and teach it to others. It may seem shocking to find out that people still remember these songs, but they have been around so long that people remember them just because they heard them a few times from someone who is much older.
The best thing that you can do is to sing to the kids so that they will be happy and learn. They will get to have a little tea time with a song (maybe throw a tea party!), and you can sing it to your kids when you are trying to rock them to sleep or comfort them.