All I know about flat frequency response is all related to microphones and how some people would like a mic that captures audio in it's purest form.
 
When mixing, I heard something that the room has to have a flat frequency response especially when using monitor speakers.

A speaker can theoretically have a flat frequency response, but once you put the speaker into an environment, the sound you now hear is the speaker and it's interaction with the environment.  It's this interaction that causes the overall frequency response to no longer be flat by the time it reaches your ears.

As sound travels, any surface the sound reaches causes some degree of reflection.  A tiled room will cause a great deal of reflection of all frequencies.  A room with thick carpet on all the surfaces will cause very little reflection and will tend to absorb high frequencies very well.

When audio is reflected, certain frequencies from the reflections add to the original signal and some subtract, causing an uneven frequency response.  A lot of factors are at play here including the types of surfaces in the room, the size of the room and where you are located compared to the speaker location.  Suffice to say, it all can get pretty complicated.

The goal then is to minimize the uneven frequency response as much as possible.  Short of an anechoic chamber, it's very hard to create an environment with a flat frequency response.  Get it as good as you can, and if your mixes translate well to the real world than you are in good shape.

so the best thing to have is a flat frequency response from the room?

Yes, though you'll never get it perfect. The small rooms that most of us have are smaller than the actual wavelengths once you start getting down into the lower octaves. So you can get huge peaks and cancellations in the bass as heard in the room, like as much as 40dB between the worst cancellations and peaks. This will wreak havoc with your attempts to mix the bass since you can't hear what's really happening.

At higher frequencies you have issues with reflections off nearby walls coming back at slightly different times, creating subtle cancellations (comb filtering is generally what's going on, a finely spaced set of peaks of cancellations.) So the room is a big issue with getting a nice sound. There's lot of discussion out ther eon the subject to read up on.
Basically you do three things:
 
1. Diffusion, to get things reflecting away from the listener in the mids to higher frequencies, or spreading out the reflections via pseudo-randomly shaped diffusive surfaces.
 
2. Absorption, to suck up bass energy and turn it into heat. Fiberglass insulation is typical for this, such as Corning 703. When they are placed an inch or so from the wall, the bass energy has to get through the insulation, hit the wall, and bounce back through again. This reduces the energy significantly so that it's must lower by the time it gets back to you.
 
You can't use diffusion for low frequences because the waves are too big.
 
3. Listening position placement. There's an optimal position for the mixing position (i.e. where your head will be when mixing), that will start you off at the best you can do before you do the things above. Given a room with X,Y, and Z dimensions, there will be peaks and cancellations are particular places along each axis. There is an optimal position where you are in between as many of them as possible, and it's typically a fairly appropriate spot as well, usually about 38% out from the wall (front to back.) That's your head position, so the desk and speakers will be between you and the wall, and that usually puts the speakers at a reasonable distance from the wall to avoid boominess and such.
 

IK Multimedia ARC Room Correction. Get it and enjoy.

Room correction systems can only do so much. They can't really do anything about bass cancellations at all, unless I'm missing something.

@ James. I took a look at the Plugin and I watched some videos about it. In their videos they said it's a combination of three things.
 
1.ARC Mic
2. ARC Software
3. ARC Plugin
 
I'm on a tight budget and I like to work with the things I have inles deemed neccesary.
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@Droddey. What is bass cancellations?
 
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Take a look at this video around 2:30 http://www.youtube.com/watch?v=uSMJ89iOJY8

There are two possible issues. One is that bass from the speakers meets bass coming back from a wall and they combine at a particualr frequency to make it louder. You can use an EQ to bring this down. But the other is when they hit and cancel. You can't fix this with EQ, because they will always cancel out.

A bit too complicated for me, but thanks!

Sound is an oscillation of air pressure, i.e. it's a series of higher and lower pressure waves propogating outwards. If two such waves hit each other where both are going up or down, then they add together, i.e. the high pressures parts combine and their low pressure parts combine. So you get a sound that can be up to twice as loud.

If two waves hit each other such that their high/low pressure parts are exactly on of sync, then one's low pressure part lines up with the other's high pressure part, and vice versa. So they will cancel each other out because, to your ears, the combined effect is nothing.

You can counter act a peak by just lowering the audio at the frequencies where the peaks are. But no matter what you do the cancellations will still cancel. You can't raise the signal at that frequency and do any good since the reflection will then come back at the higher level as well and they'll still cancel out.