Profiles are the files which adjust your monitor, scanner, digital camera and printer to bring these devices into line with a common benchmark. Or more accurately, a series of benchmarks - as there are several options for some devices. Such as Gamma, Colour temperature and Luminance of a monitor.
This enables your 'system' to be colour managed, the outcome of which is that you can 'soft proof' - view a simulation of the print on your monitor to see what the print will look like. At this stage you can choose a number of options to fine tune the way it is rendered to meet your preferences - or choose the best compromise if colours are out of Gamut.
It also enables you to send files to a 3rd party and know that they will print as you would wish and as you see the image on your own monitor.
There are Generic profiles provided by manufacturers and others which may get you into the correct ball park. Custom profiles are made specifically for your devices - they can be significantly better. However it depends on the skill of the operator!
You can buy the gear yourself and it is getting cheaper, or pay someone to do the work for you. A monitor calibrator is cheap and ought to be done a least every 4 weeks. To calibrate other devices, they oughtn't drift and if you don't use many paper types, is cheaper to get this done for you.
I cannot stress enough how I consider this to be an essential part of incorporating a digital element in your imaging process. To not do this causes endless testing and other headaches. I've had them!!
Consider it as the equivalent of a Band/Orchestra tuning up before a performance. You want your prints to sing!