The graphs show the volume of the sound vs the frequency, ie how loud each frequency is.
So I guess the 'holy grail' is a flat in room response, at the main listening position (MLP) or, even better, across all of the seats. This way the individual's room and speakers are taken out of the equation and and bangs, crashes and zipping xwings are reproduced as intended in the studio.
However, human hearing is not a flat line. Particularly with age we get less sensitive to high frequencies and we are also relatively insensitive to low frequencies below 20Hz, which we often feel more than we hear.
We also are also relatively insensitive to changes in volume of less than a few dBs, and less aware of these volume changes the slower they happen. We are also more aware of large peaks in volume than dips.
So! Putting all this together we aim for as flat and smooth a line as possible from 20Hz to 20kHz. The common feeling is that a flat frequency response line (eg 85dB from 20Hz to 20KHz) does not sound right in a small room, as in most homes - so the target line is often tilted slightly 'downwards' so that the bass is slightly louder than the treble.
The graphs show uncorrected frequency/volume responses for the MLP for all speakers together, and each individual speaker, as well as my and YPAOs attempts to flatten/equalise each raw response through filters.
With software like DIRAC it is possible to get near perfect flat target 'curves' (or lines really!), but all the myriad tiny peaks and troughs in response are impossible to equalise with only 7 filters per channel.
In reality given the relative insensitivity of the human ear, you can argue that we do not need to achieve a ruler flat response, and the commonly accepted wisdom is that a response of +/- 3dB is pretty damn good and likely to sound very smooth. A response of +/-10dB or greater is likely to be perceived as quite a bit rougher, with large swings in volume at different frequencies and therefore less cohesive and natural.
All my graphs with peaks and valleys have the scale set to show those features more easily - if the scale was 0dB to 90dB for example, it would look like a nearly flat line.
All room correction software does its best to get the response to these targets. Some does better than others.
I thought I could do better than YPAO certainly but given the limitations of the yamaha PEQ it is difficult and YPAO does about as good a job as I could expect (or manage myself) with the tools that it has.
Whether any of this REALLY makes a significant difference in listening enjoyment is up in the air, and there is certainly at least a modicum of placebo effect but hey, part of the fun is setting it up and tinkering to get the sound 'perfect', even if no one else can tell the difference!
Anyway I hope that was moderately useful and explained what these room correction graphs are all about