The system is looking for the amd64-microcode package. This is firmware needed by hardware on your system. Ubuntu does a great job of detecting your hardware and in most cases installing what's needed, but it's not foolproof.
If you have been using the system for 3 weeks and this problem just started, most likely the kernel was recently updated, and the new kernel has to have this package. New kernels are installed by Software Updates. You may not have realized that a new kernel was installed.
It's always possible that a newly installed kernel breaks something. When this happens you can boot from the older kernel until you figure out what you need. In this case, it looks like the system needs you to manually install that package, which is easy.
First try to boot from the older kernel
The boot menu is handled by Grub2. When a new kernel is installed, it makes the new kernel the first choice and hides all older kenrels behind the menu item "Advanced Options for Ubuntu".
If Ubuntu is the only operating system on the computer, you may not see the Grub2 menu by default. To see it, hold down the Shift as the system boots.
When you see the Grub2 menu, use ↓ (the down arrow key) to move down to the advanced options, then hit Enter. You will see one or more boot options with an older kernel. Choose one, and you should boot ok.
Install the package
It can be hard to find technical packages in the Software Center. The easiest way to do it is to use the terminal.
Ctrl+Alt+t will open a terminal. Copy and paste:
sudo apt-get install amd64-microcode
If for some reason you don't see other kernel options or still can't boot, you should see an option in the Advanced Options choices that ends in (Recovery Mode). Choose this. After it starts to run, you will see a dialog with various recovery choices.
First try Resume. This may allow you to boot without the problem you were having. If this works, install the package from the command line as above. Be sure to reboot afterwards.
If you still can't boot, try again and this time choose Root from the recovery dialog. This will drop you into a command line for root. You will be able to install the package but be careful when working as root. Be sure to reboot afterwards.
If none of the above work, you may be able to install the package using chroot from the live cd. One use of chroot is change the root environment from the LiveCD to the installed system hard drive you need to target. (This is usually on the hard drive, but could be on a usb or elsewhere.) In short, you are using the Live medium to boot a broken system that won't otherwise boot. This is a little more complicated but is not hard.
1) Boot from the LiveCD/USB you used to install Ubuntu (or at least make sure the live medium and the installed system have the same architecture - both 32-bit or both 64-bit). Use Try Ubuntu.
2) Open the terminal.
3) Mount your Ubuntu root partition:
sudo mount /dev/sdXY /mnt
X is partition letter and Y is the partition number.
If you followed a standard "Replace Windows", I believe you will have /dev/sda1 as your root partition.
If you are not sure, the following commands may help you figure it out.
sudo fdisk -l
If you are realy stuck on this part, you may need to ask for more help.
Let's assume root is on /dev/sda1
sudo mount /dev/sda1 /mnt
4) You then need to mount various parts of the filesystem. The Ubuntu Community page for resintalling GRub2, has a nice single command to handle this.
for i in /dev /dev/pts /proc /sys /run; do sudo mount -B $i /mnt$i; done
5) Chroot into the installed system with
sudo chroot /mnt
6) Install the package.
apt-get install amd64-microcode
You will be at a root prompt, so you won't need
sudo. As always, be careful and reboot as soon as you are finished installing.