An ICC profile helps you get the correct colour from a device, but it's a bit of a black box, data goes in and comes out without any hint of the process involved.
Consider how a profile is created.
You print out a colour swatch like this one, it's about 800 colour swatches with various CMYK formulae.
It is read by a spectrophotometer which records the actual colour that is on the paper. Now, we know the CMYK values for each swatch and we know the colour of that swatch.
So if we want to reproduce that colour, we have a CMYK formula, this is stored in a Look Up Table (LUT).
Simple really.
What is an ICC Colour Profile?
What's behind the Photoshop settings?