Wow this was an old question, but you never know, maybe it could help someone.
Wavelets aren't easy to get an in-depth understanding of very fast. Wavelets are functions which are self-similar at different scales. There is a father and a mother wavelet. The father wavelet captures in some sense low Fourier frequencies (especially mean values - "DC" level) and the mother wavelet captures in some sense high Fourier frequencies. For the discrete wavelet transform there is a recursive relation between the filters and the wavelet functions which make fast transformation possible - instead of having to use larger filters for the lower frequency bands we can use redundancies deliberately introduced in the construction of the wavelet to speed up calculations a lot. You could in some sense compare this to fast Fourier transform (which actually builds on the high-school relation between sines and cosines) allowing fast transformation using the Fourier transform.
For each new scale level of a wavelet transform you get
- a bunch of details (captured by the mother wavelet - the wavelet filter) and
- a coarser version of the signal (captured by the father wavelet - the scaling filter).
Then you iterate on 2 -- the coarse signal, finding details for the next scale level ending up with an even coarser signal and so on.
If you want to learn this well you will need to spend time on it. It is enough of a challenge implementing the algorithm on a short time frame, but there really is lots of theory to really understand it and not only be able to use it.