Here's a summary:
Two somewhat disgruntled children, Tyltyl (the older girl) and Mytyl (the boy) after wishing Christmas would be better for them (their parents are poor and cannot afford all the presents and wonderful food that other richer people are indulging in), are sent out by the fairy Bérylune on a fantastical trip into various lands (Land of Luxury, the Past, the Future etc) to search for the Bluebird of Happiness. They are accompanied by their dog and cat (given human form by the fairy - who also gives other objects like milk, sugar, light and fire a temporary human form), the characters of which provide their own complications to the search along the way. Finally returning home empty-handed, the children see in the light of the new day that the bird has been in a cage in their home the whole time. Tyltyl, having found happiness in herself, gives the bird as a present to a sick neighbor but the bird escapes to freedom.The story was made into a play in the early 1900's by Maeterlinck, which was very successful and popular, and has been made into more stage adaptations, including ballets, as well. The play has also been made into a film a number of times: two silent films, another in color (which is the most famous, with Shirley Temple as Tyltyl) in 1940, another in 1976 (with Elizabeth Taylor, which I saw as a child) and later as a Japanese anime. Three of the films are now available on DVD (you can see a lot of images from all three films HERE).
The story is very much about teaching the value of family, love and 'the journey' (not 'getting the prize') and the importance of sharing and giving but despite being overtly didactic in this manner, the films and story have a lot of charm and all these 'lessons' contribute greatly to the overall Christmas and New Year feel.
As a child, I especially loved all the objects coming to life, the spirits of the forest/trees, seeing the children who were about to be born and the personified cat and dog and must admit these are still big draws to the tale for me today.
You can read the whole version (in prose, as written out for children from the play) HERE.