If you imagine sticking your hand out of the window of a light aircraft the EAS is the force you would feel on it, the wind, if you like. As you go higher the air gets thinner so, to get the same force on your hand, you have to travel faster. You have a higher true air speed. Air speed indicators measure the force, so indicate something close to EAS rather than TAS.
The Mach number is a fraction of the local speed of sound. The local speed of sound expressed as a true air speed is lower at lower temperatures. The air gets colder as you go up. This means that, as you climb (at a constant EAS), you get closer to the speed of sound (your Mach number rises) because the TAS increases and the speed of sound gets lower.
That's a bit over simplified....more if you wish?