It's not a stupid question.
Privilege levels in an operating system
Ubuntu - and indeed any modern operating system - has the concept of different privilege levels for different software. Software initiated by users usually runs under a user-based privilege level, which for security reasons does not have the required access to modify the system - it can only modify files belonging to that user.
In order to perform any modification to the operating system which could have an impact on the system as a whole, rather than just the user's files, a higher privilege level is required, which in Linux is referred to as "superuser" privileges (or commonly called "root"). This privilege level has unfettered access to the entire operating system allowing it to modify - or destroy - all files for all users.
The role of apt-get
When you are installing software via apt-get, you are installing software that will be available system-wide. That is, the software won't just be placed into a user's home directory for running by that user only, but it will be installed in a system-wide application directory (such as in /usr, /etc, /var and so on) for running by all users. In order to modify these directories you need superuser privileges. No unprivileged user can modify these directories, because otherwise unprivileged software could mess with the system.
If you try to install something using apt-get without giving apt-get superuser privileges, the first hurdle that it will fail to overcome is to obtain a lock to write to its own software catalog. Being a system-wide utility, apt-get maintains a catalog of installed software, which naturally requires superuser privileges to edit so that unprivileged software can't mess with it. But even if you could somehow overcome this hurdle (for example, by changing file permissions), many further steps along the way of installing the software will still fail, because the installation routine will depend upon writing to several system directories.
Using Linux it is possible to install software without superuser privileges, but you need to write it yourself (eg, shell scripts) or compile it yourself and run the compiled executables directly. It is easier just to install it system-wide using apt-get (and other APT based utilities like aptitude, synaptic, or the Ubuntu software centre) if you have access to do so.