A partial upgrade is sometimes required if certain dependencies of packages changed during an update. It will not upgrade you to any other Ubuntu release, unless you've manually changed your apt sources to point at a newer release.
If you choose Continue in that dialog, you should see the list of packages to update. Some of those may not be selectable. What Partial Upgrade does, is the extra bits necessary to resolve the dependencies of those packages. Usually, it means installing a new package or two.
It is perfectly safe and normal for this Partial Upgrade request to happen, depending on the packages you have installed.