Topaz is an ebook format Amazon uses to quickly convert scanned paper books (e.g. from its look inside the book) to ebooks. It is in principle an interesting approach to ebooks, since it does reflow and can be searched even though it is very "close" to the paper original. However, in practice the quality of what you get on the screen is highly variable - sometimes beautiful typography but much more often unreadable (if you are at all sensitive to typeface blemishes).
So I have been avoiding Topaz ever since I got my Kindle 1. More recently I switched to non-Kindle devices and the weirdness of Topaz prevented DRM stripping and easy format conversion. Heroic efforts of reverse engineering made conversion to other formats possible over time, but I still considered them too "hands on" for routine use.
This is a major issue, because when there is a Topaz it is very often the only legal ebook version available.
I am delighted to report that, in my opinion, Topaz format shifting is now "good enough" so that you need not worry about whether a Kindle ebook is AZW or TPZ if you are buying it for the purpose of format shifting to an ePub-based reading device. As usual Apprentice Alf's Blog is the place to go to explore DRM issues. I use stand-alone DRM-stripping tools and the Calibre ebook-convert command line, but the 3rd party Calibre plugin for MOBI/AZW/TPZ will be the easiest approach for many. In fact, if the Topaz looks crappy on your Kindle device/app screen you may be better off having Calibre convert it to MOBI.
The only downside of the conversion is that it produces three ZIP files, and the 2nd and 3rd are very big. I only use the 1st one, which is based on the OCRed text. Conversion isn't perfect. Some bolding and italics are lost, chapter headings are often images (which prevents Calibre from detecting chapters for the TOC), and frontpiece material is usually images and can be poorly laid out.
I bought half a dozen Topaz ebooks by mistake over the years, and they have sat unread. I also had a long list of Topaz ebooks on my wishlist, on the off chance that they got replaced by a AZW (which does happen occasionally). Many of these are now sitting on my ebook reader as ePubs. Spot checks have not unearthed any problems, and the two I have read were almost perfect (fewer OCR errors than the typical AZW from paper).
Have my low expectations got the better of me? I don't miss bold and italics much, and I hated bad typefaces. I would still buy the average AZW or ePub over the TPZ any day, but when the Topaz is the only choice and a really want the ebook it is now a viable option.