The ICC (international colour consortiumn) many years back developed a system to predict how colour would print before the expense of printing (in 4 colour for magazines and the like)
There are two types of profile - output and working.
A working space relates what colour is seen for a given value of RGB - as the numbers don't mean anything without this... so 127R 127G 127B is a middle shade of gray and so on...
The purpose of the output profile is to map how the image transfers to paper (or screen) so that it compensates for the transfer, so that each defined colour prints as the correct colour. The differences can be caused by how the ink is absorbed into the paper - how the ink has been mixed, how the printhead put the ink through, even the relative humidy and temperature will have effects...
The same is true for your screen - you put a device on your screen to correct how bright and contrasty it is, and the colour temperature etc... This is one essental - as we will always think that the screen is right - and often people will take a perfectly exposed and balanced file from the camera and then mess it up. As a default your screen is too bright and too blue - so if your print come back too dark and yellow this is the cause.
Printer profiles can be downloaded from the paper manufactures website - and these will often be very good - but not perfect as they don't represent your printer but an average of your type of printer. If you make your own with a good bit of kit they will be more accurate.
If you send your work to a lab they will do all this hard work - so all you have to do is get your screen right.
Some labs, like One Vision, Colourworld, Loxley specify the working space your work should be sent in - normally sRGB as this space is closest to what photographic printers can print.
I run a small lab that uses the same production software and the way we have ours set up we can accept any working space - but if there is no profile we assume it to be sRGB
Other labs ask for you to embed their printer profiles as they don't use lab production software.
Now within Photoshop you can "soft proof" where you can see how your image will appear printed with a given output profile and printer - however with many larger labs who have a number of different kinds of printer you might not be able to do this as you won't know which printer will be used for your job.
Unless you have spent around £1000 for your monitor and calibrator - and as importantly have the correct working enviroment of brightness in the room, wall colour and correct tubes in your light fittings - you will not get an exact match every time.....
But it will be much closer!