Drupal7 was launched in January 2011. About 7-8 months later, we are now able to practically use it for web projects. Important 3rd party modules such as 'Views' were now available & stable in Drupal7. So any web project that go for a complete revamp/re-design of existing drupal sites also look for upgrading to Drupal7. New drupal projects naturally look to use the latest major version available.
Drupal7 is definitely a step up from Drupal6. It's more elegant & many vital features that were covered by add-on modules were now built into the core. Using it is a breeze. But it also demands certain features of PHP & a latest version of MySQL, that many web servers do not provide.
Apart from the standard requirements needed to run Drupal6 such as PHP Register Globals should be off etc., Drupal7 requires Mysql 5.0.15 (or higher) with 'PHP Data Objects' (PDO) enabled.
If you are running your site in the same server for say 2 - 3 years, chances are this is not enabled. Enabling it in MySQL is a major work & previous databases may not work correctly. Expect a service outage of up to 3 hours for your website. And, if you are in a shared server, you can forget asking your web host to upgrade. They wouldn't risk corrupting databases of 100s (or even 1000s) of websites for the sake of 1 client.
Do check these requirements. More details of Drupal7 requirements are here. Sometimes, you may need to migrate to a different web server.
Upgrading to latest version in Drupal has a different meaning than say, Wordpress. In Wordpress, if your website uses Ver.2.9 or lower, upgrading to 3.0 or higher is a must from security point of view. In Drupal, if your website uses Ver.6.21 or lower, you should upgrade to 6.22 (currently the latest in 6), but upgrading to 7.x is not necessary & in several cases not feasible.
In short, you can & should upgrade to latest minor version (after the dot in version number), and upgrading to latest major version in Drupal is almost like moving from one CMS to another.