sudo apt-get update just updates the Package Index lists - the lists containing information about which packages and in which versions are available. It does not update any software package, but it is the prerequisite for doing this.
To do the updates that were found by running
apt-get update, you need to run:
sudo apt-get upgrade
It will compare the installed package versions with the available versions (from the list you updated with
apt-get update) and install the newest versions of all possible packages.
If some packages require the installation or removal of additional packages to get updated (like the kernel for example), you need to run the following command afterwards:
sudo apt-get dist-upgrade