When talking about computers, the term "multimedia controller" can be used to describe a few different bits of hardware depending on the make and model of your PC. Basically, it's a piece of your motherboard that communicates with different hardware, but there's a bit more to multimedia controllers than that.
Most computer users will never have to worry about their multimedia controller, as it's a device that is automatically configured by the system's management program and by the operating system. In short, a controller or controller card is the go-between for the motherboard (or system board) and the expansion cards for a system. In a desktop computer, this applies to video and sound cards; for a laptop, the controller communicates with the onboard multimedia devices.
Occasionally, after reinstalling your operating system, your system may identify an "unknown device" in its device manager and list it as a multimedia controller. Specific drivers vary from system to system, and most newer computers and operating systems automatically detect the multimedia controller. Computer manufacturers will list a chipset driver or multimedia driver on their websites if it's necessary to install.
If you have a desktop computer and plan to upgrade your sound or video card, it's a good idea to first upgrade your multimedia controller (or chipset) driver to the newest version, then install the newest drivers for the new device as soon as you have inserted it.