LZMA is an improved version of famous LZ77 compression algorithm. It was improved in way of maximum increasing of compression ratio, keeping high decompression speed and low memory requirements for decompressing. lzma command line tool has a similar interface to gzip(1) and bzip2(1) and is intended to make use of LZMA compression easy for the users who are already familiar with gzip and bzip2.
Another issue I see on the message boards quite frequently users are trying to get their heads around tar archiving utilities, and gzip/bzip2 compression utilities. It pays to keep in mind that in the Windows world both of these are packaged together in the .zip format. In the Linux world, as with most things, more control comes at the price of more complexity, as the two issues of archiving and compression are separated.
I guess the first thing we should do is discuss the difference. Compression is a means to shrink the physical size of a file in bytes. The technical aspects of how compression works is a bit beyond the scope of this guide, so suffice it to say that the computer uses an algorithm to combine redundant bytes of data together. Archiving on the other hand, is the act of combining several files together into one, for ease of backup and distribution, all the while keeping the individual file attributes and permissions intact.