Colour Grading (sometimes called colour timing) is the process of giving a video a aesthetically pleaseing in look. This can range from a totally natural look tO highly stylised ones. It generaly starts by getting the levels (blacks/whites/exposure) correct then moving onto setting the colour (often starting with something similar to colour/white balance). On a profesional level this involves using a reference monitor (costing thousands or pounds) or a Philips Plasma (which works well and is a lot cheaper but the smalest are 42″). Whatever you use these have to be properly calibrated (generally to Rec.709).
Balckmagic Davinci Resolve
Resolve is the software of choise for many Film and TV graders. The full version with Blackmagic Control services is oner £20,000 but there is a free version (with very few restrictions, the main being can only use one GPU, only go up to 2k and does not have noise reduction, basically all you need to indy film & video making). There is also a £700 full version without the control services and 3rd party control services can be got for around £2000.
F Stop Acadamy have 4 introductory videos, alough they show using Resolve with a control service more of what is here is still relevant if you are not using one (alough you may wish to skip the first).