Your boot partition is full. Since this is a kernel update,these files will be copied to the boot partition so you need to clean in out. Here is ablog post that will show you how to clear the old kernel images with one command. I'll give a basic synopsis of the method. Use this command to print out the current version of your kernel:

uname -r

Then use this command to print out all the kernels you have installed that aren't your newest kernel:

dpkg -l linux-{image,headers}-"[0-9]*" | awk '/^ii/{ print $2}' | grep -v -e `uname -r | cut -f1,2 -d"-"` | grep -e '[0-9]'

Make sure your current kernel isn't on that list. Notice how this is the majority of the final command (down below). To uninstall and delete these old kernels you will want to pipe these arguments to:

sudo apt-get -y purge

Now we can do everything we want by combining these last two commands into this unholy mess:

dpkg -l linux-{image,2 -d"-"` | grep -e '[0-9]' | xargs sudo apt-get -y purge

And that one command will take care of everything for you. I will confirm that this does work perfectly but never trust anybody on the internet. :) For more info,the blog post gives a very good explanation of what each part of the command does so read through it so you are satisfied that it does what you want it to do.