If you're using something like a DSLR gain is probably expressed as ISO instead. Regardless of which term is used, in a video system it basically describes the process of applying amplification to the signal which is coming from the photosites on the sensor. Amplifying the signal allows you to boost low signals (low exposure) to raise the overall brightness of the image - but it also raises the noise present in the signal as well. Thus, higher gain/ISO results in an overall noisier image, while low gain/ISO results in the noise dropping low enough that it tends to disappear below the visible threshold in the shadows.
In terms of noise reduction it mostly just means you'll need to apply more at higher gain/ISO settings - how much depends on the camera, lighting, and choices made in grading. If you're using something like Neat video which lets you build noise reduction profiles you may get better results if you build a profile which matches the gain/ISO setting on your camera, as the effect on noise isn't always linear with increases in gain/ISO.
Some cameras have noise reduction on board, which you may or may not be able to control. In general, if a camera uses a lossy codec like h.264 (avchd) you may get better results in camera because the noise reduction can be applied before the compression - codecs can have a difficult time differentiating between noise and detail in an image. With a higher quality codec on board (i.e. ProRes, or raw video) you'll probably get better results in post, because you aren't limited to what the on-board processor can handle in real time. This is why cameras like Blackmagic's don't do on-board noise reduction.
If you're looking to get the best results it can be useful to test your camera by shooting black at various gain/ISO levels and then boosting the signal in post to examine the noise profile. For instance, Canon uses a mix of actual gain and digitally pushing/pulling the signal to create some of the intermediate ISO settings, so the noise may or may not change as expected. Additionally, the 5DmkIII appears to kick in a higher level/different type of noise reduction at around 1200 ISO, so the fine noise changes dramatically at that point compared to lower ISOs.