Remote access is just what it sounds like -- the ability to access your computer from a remote location. Programs like PC Anywhere (Windows), Remote Access (Mac), and Timbuktu (Windows and Mac) allow users to control remote computers from their local machine. In order for a remote access connection to take place, the local machine must have the remote client software installed and the remote machine must have the remote server software installed. Also, a username and password is almost always required to authenticate the connecting user.
Remote access is more than just being able to connect to a remote machine -- it is the ability to control the machine once the connection has been made. A remote access program can basically transform your local computer into the the remote computer you connect to. This is great for people who sometimes work from home and for server administrators who frequently need to update and make changes on their server machines. Most remote access programs also allow users to transfer files between the local and remote machines, which can save a lot of commuting time. While remote access can be helpful for many people, don't enable it on your machine unless you absolutely need to. It is just one more security concern you will have to deal with.