Three is read as synthesis and creativity — two things meeting to make a third. Fairy tales do things in threes, so tradition also links it to completion and to the moment when something finally works.
Does the traditional reading fit your dream, or did it mean something else to you?
My Cosmic Code has a private dream journal. Write a dream down and the app picks out the symbols in it, shows what dream books say about them and, over time, which words recur across your entries. The journal is stored on your device only.