A clean install is a software installation in which any previous version is eradicated. The alternative to a clean install is an upgrade, in which elements of a previous version remain.
The terms are often heard in reference to operating systems. A clean installation of an operating system formats the drive and erases all existing data -- the user has to back up all data beforehand. Applications will have to be reinstalled, as well. An upgrade, sometimes referred to as an "in-place install," retains user data and settings.
There are pros and cons to both clean installs and upgrades. An upgrade is typically less expensive, for example, but because elements of the earlier version and other sofware remain, any existing performance issues may remain as well and new compatibility-related issues may arise. A clean install should make the computer's software run like new.
A clean installation of a newer version of the existing operating system is sometimes referred to as a clean upgrade.