What does a relay do?
i missed this question in my first reply
a relay will close a circuit between 2 of its terminals based on a command given to another set of terminals. so to put it in plain english, when your temp switch reaches a certain temperature and closes it's internal circuit will give a ground to it's connector terminal - that ground will be used to close the relay circuit which in turn will power the fan - this is because the temp switch for example could have a rating of 1 amp for its internal contacts and your fan can draw 25 amps - that means if you wire the fan thru the temp switch directly it will destroy the internal contacts - by using the relay you isolate the high current (amperage) thru the relay only, and the temp switch load will only be used to activate the relay solenoid. the temp switch is also known as an electrical thermostat or bimetallic electrical thermostat (not to be confused with the water thermostat that goes before the radiator, that is a mechanical device). There are also adjustable devices that use a temp probe an in that case you can adjust the temperature at which the fan turns on (more specifically at which the command circuit will close) - you can buy one of those and they usually come with a relay wired in, so it could be easier to install but make sure that the relay amp rating covers (is at least) the amp draw of your fan. The temp switches have a set on and off temperature. There is also a company that makes an electronic device which controls the speed of the fan based on the temperature - some guys here have used their product with excellent results (i have not used one personally) - the name of the company is Delta Current Control.
The idea of using a relay is the same for the manual switch (which is used instead of the temp switch).
Since you asked what is a relay I suggest you ask for some hands-on help with this one and don't attempt to do it on your own - you will also need to have matching wiring (that will be rated to support the current drawn by your fan), matching fuse for the power terminals of the relay and if you are not using a fused connection for the solenoid of portion of the wiring (command terminals) you will need a fuse there too.
Like Jeffy said, last thing you want is an electrical melt or fire, so the first time you attempt this you should do it with the help of someone that has experience with automotive electrical wiring.