Boy have been asking a bunch of questions on here lately, I have always been curious about this other driver called the CPU Microcode driver, I have an intel i3 Core Processor. I understand that this will increase your CPU performance with Ubuntu pretty well, but I'm not sure if I should install it.
Actually, whether you have to install the intel-microcode package or not depends entirely on your firmware, and what processor you are using.
If you are using anything newer than a thrid-gen Core, you need the newest microcode to avoid several errata. It is much worse on 5th gen and 6th gen, where you are guaranteed to have crashes and data corruption due to issues on Intel TSX, AVX/AVX2, virtualization, and power management that were fixed in the latest microcode updates, but even 4th gen processors will misbehave badly when using older microcode.
Basically: install the intel microcode update package unless you really know better. The newer intel processors have a LOT of functionality defined or parametrized in microcode, and should be treated just like any software package that had receives critical fixes often: keep it up to date.
The issues that Intel has been fixing lately in public microcode updates are everything but minor. They fix at least one critical issue per public update.
Installing a microcode update is generally a good idea, as it can fix known problems or vulnerabilities in your CPU. While these can be patched with a BIOS/UEFI update, doing so in Ubuntu as well adds additional assurance that the patch is effective and can help you make sure it is patched sooner.
The microcode in a CPU is basically a translation layer between machine code from your software and the inner workings of the CPU. It teaches the CPU what to do in response to machine code instructions. An update may be installed in your BIOS/UEFI interface, and it can also be loaded by your operating system at boot. In addition to fixing bugs or vulnerabilities, an update may sometimes negatively or positively affect performance, though not often in a significant way.
Note: I updated this answer because it was originally written in 2016 before CPU security flaws such as Meltdown and Spectre were known and before I started thinking of microcode updates as important for security.