What exactly is VMO and how does it affect a plane when it is exceeded?
$V_{MO}$ is a “maximum operating speed”. It is one of many “V-speeds” defined for an aircraft that limit operation at various flight phases. All V-speeds are indicated airspeeds¹.

The $V_{MO}$ is the maximum permitted speed for the aircraft. This includes a safety margin, so pilots can reasonably fly near that speed. Exceeding it is not immediately dangerous, but as it reduces safety margins, is an incident that should be investigated.

There is another speed, $V_{NE}$, the “never exceed speed”, which is somewhat higher and which marks the point where things start to get dangerous. When the aircraft exceeds $V_{NE}$, aeroelastic flutter may develop that will destroy the aircraft and/or important parts may break off as the dynamic pressure becomes higher than what they are designed for.

Also these speeds have their Mach number counterparts², $M_{MO}$ and $M_{NE}$. At high altitude, the same indicated airspeed (IAS) corresponds to much higher true air-speed, since indicated airspeed decreases with pressure, while the same Mach number corresponds to slightly lower true air-speed, since speed of sound only depends on temperature. So at high altitudes, the Mach limits are reached first while at low altitudes the IAS limits are.

Exceeding the $M_{NE}$ has different effect, though also dangerous. Above that speed flow separation occurs above the wing due to supersonic speed of the flow. This leads to loss of lift and significant down-pitching moment (a.k.a mach tuck), which aircraft not designed for supersonic flight may not have enough elevator authority to compensate.



¹ The airspeeds are given as IAS, the speed measured by pitot probes, so they can be directly compared to the indication in cockpit (aircraft with EFIS (“glass cockpit”) usually correct those measurement errors that can be estimated, showing so called calibrated airspeed (CAS)). However it may not be just a simple number but may be tabulated depending on other parameters.

In particular $V_{NE}$ and $V_{MO}$ may depend on altitude, because flutter depends on true airspeed (TAS) and at lower density (due to lower pressure at altitude) the same TAS corresponds to lower EAS/CAS/IAS.

² Mach number is true airspeed as fraction of speed of sound. In this case the limiting factor is formation of shockwaves due to the flow speed locally exceeding speed of sound around some parts of the aircraft.