The purpose is the same as any other indicator, to analyze the price series and determine information about its recent movement that can assist in making informed trading decisions.
There many reasons why wavelets are superior to other techniques for analyzing market data, however in order to realize many of their benefits you must understand what the benefits are and how to use them to your advantage.
In fact, one of the main benefits of wavelets is that there is a huge amount of instructional material out there which you can use to learn exactly how to use them.
You can go to any trading forum and find hundreds of methods of how to use various indicators, however very few of the people who create those methods have a deep understanding of the mathematical basis of the indicators they use. Thus the methods that they create, if they work at all, are usually tied to a very specific timeframe or instrument and set of parameters, and for that reason the likelihood of them continuing to work for any period of time is relatively low.
Contrast that with wavelets where you can easily find information on how to use them to analyze any type of data, written by people who really know what they are talking about and understand the implications of using one analysis technique versus another. To get that kind of quality information and training about how to use a trading-specific indicator you would have to pay out the nose (and even then it would almost surely be subpar compared to what is available free/cheap for wavelets)
Also, as I have mentioned before and you can see from websouths screenshots above, Guppy MA technique is essentially the same as the haar transform. So any of his material is applicable to Haar wavelets as well. The reason that wavelets are superior to GuppyMA is because they don't require you select your own set of periods, and the set of periods they use (powers of 2) can be proven to encode the maximal amount of information in the lowest amount of lines, so less unnecessary information to analyze and less computational power. Guppy MA does look cool with lots of lines though, can't deny that ; )