What is the CiviCRM LTS Version, and should I use it or the latest stable release?
LTS stands for Long Term Stable version. It is intended for use on more conservative sites that are more concerned with having a stable CiviCRM environment than with having access to the latest features in CiviCRM. You should decide which type of site yours is.

The LTS version contains all fixes for security vulnerabilities that affect the software, and many but not all of the bug fixes that are available in the stable version. As mentioned, it does not contain the new features made available in more recent versions.

The LTS version tends to be one or two minor versions behind the latest stable version. So a little while after 4.5 was released as the latest stable version, the LTS version switched from 4.2 to 4.4, skipping 4.3. Similarly, in late 2015 likely after 4.7 came out, 4.6 became the LTS version, skipping 4.5. Now that it is April 2016, the expectation is that 4.7 could become the next Long Term Stable release after 4.6, in anticipation of significant changes in 5.0.
But the final decision on this won't likely be made until late 2016 / early 2017.

The benefits of using the LTS (long term stable) release are:


There are fewer unknown bugs in the software since it has been used extensively for a long time.
Upgrading within one release branch like 4.2 or 4.4 is less likely to require extra effort or cause problems than upgrades from 4.2 to 4.3, or 4.4 to 4.5. 


Downsides to using LTS include:


Not having access to the features available in more recent versions of CiviCRM.
Not having access to extensions or releases of extensions that are only available for more recent versions of CiviCRM.
Not having access to some bug fixes that are included in more recent versions of CiviCRM (usually ones that are not important or that require a lot of work to backport).