The easiest way to think about it is with an imaginary drum hit. The graph I posted above will be handy too.
Imagine this drum hit is so perfect that it is absolute silence before the hit, and absolutely every frequency contained in the hit starts from zero, going in a positive direction on the y axis, at exactly the same time. It sounds tight and sharp as a motherfucker, absolutely perfect. The greatest drum hit ever. You don't want to change a thing about it. But you decide you are going to eq it anyway, cos some dude on the internet said you always have to eq everything.
So you start digging with really tight boosts and cuts all over the place, where some internet frequency chart said you should cut/boost. Plus, you always have to find the bits you don't like and get rid of them totally, at least as far as that eq unit will let you, right? Best wang loads of bits out then. And you always have to boost 200Hz right, cos some other bloke said so.
Right, now you have a perfect drum hit, eq'd to.... well, eq'd. But think about the relative timing (correctly; phase) of all those little sine waves that made up the original hit. They all used to start on the 'B' of the BANG. Now you have shuffled them all about. You did a really tight boost at 1kHz, and whereas before they were pretty much in line together, now 900Hz and 1kHz are somewhat out of sync, and similarly for 1kHz and 1.1kHz, and further above/below. They were coherent before * , now they are not. Before you had a race where everyone started at exactly the same time, now they are in effect starting at different times. More accurately, they are starting from different places. To put it another way, you have smeared things in time. And that's the last thing you want for a drum hit.
[for the geeks]I know this isn't quite accurate BTW - it is just a slightly easier way to understand it. Things aren't exactly delayed in time in this way. They start at the same time as they did, but at different points in their wavecycle. The only difference between a time shift and a phase shift is that one needs a reference/origin point in order to assess phase shift. The effect is basically the same though, that some frequencies are now starting part-way through their wave cycle, some are heading downwards from zero, some are as they were, etc etc etc[/geeks]
* though due to their different periods/wavelengths they would drift in and out of sync, for the pedantic