The word "digital" is used in many different ways when it comes to digital television.
Any TV, video or set-top box you have in your home is digital. That is to say that some aspect of it uses "something digital".
Just to add to the confusion, there are "digital systems" around too. So anything from Ceefax and teletext to NICAM can be called "digital" quite correctly.
However, overall term "digital television" refers to the system of using "digital technology" to allow several TV channels to be broadcast (on the air, though cable networks or via satellite) in the same space that a single one was.
Freeview is the name of the "digital television though and aerial" system in the UK. It carries over 30 channels. To receive these channels you need either a Freeview set-top box or an "integrated" Freeview TV.
In most areas, you can continue to use the same TV aerial connection for Freeview as you do for your normal TV; in others a "digital wideband" one is required. This is called a "digital aerial" by some people.
The "set-top box" (or the same circuits in an integrated digital TV) connects to the aerial and to the TV (via a SCART connection). The computer software in the box tunes into and lists the Freeview channels automatically, showing on the TV screen details of the currently showing programmes. Within minutes you can be watching more than 30 channels, just using the new remote control.
If you have a "widescreen TV" you will also find that programmes on most channels are now shown in high-quality widescreen (without borders or stretching).
A "digital aerial" alone will just improve the chances of an easy Freeview installation.