As others have said above, it is basically a paid service where you meet with someone, and they have a massive "swatch" book of fabrics in a huge range of colours. It's a bit like those carpet swatches you can get, but way bigger, and with cotton or silk as the fabric.
They then drape each colour over your neck, so it looks a bit like a bib.
The aim is to discover which colours suit you the most, and which look fucking hideous on you. Sometimes they will give you a mini swatch book of your colours afterwards to help remind you when out shopping.
Again, some consultants will try and pigeon hole you into a certain "season" (winter, spring, summer, autumn), depending on which colours suit you the most. Some people are in between seasons of course.
You can watch demonstrations of people getting it done on youtube.