To understand the effect a magnet has on a monitor, you have to understand how a monitor works.

A monitor, or CRT (Cathode Ray Tube) monitor, works by electro-magnetism the electrons are emitted from the Cathode electron gun, and are attracted to the high voltage Anode Screen (A) they are deflected from a straight path to anywhere on the surface of the Anode screen,  by passing through an electro-magnetic field  which is done via the defection coils.

By placing an external magnet next to the monitor, (for example, a speaker which has a very powerful magnet), it causes the electrons to be attracted to the magnet and be dispersed, not hitting the Anode screen where they should (B).

The effect of this has on the monitor is to cause fogging of colour bleed and will, over time, damage the tube and shorten its working life.

SO in other words if you have speakers next to a CRT monitor simply move them further away and there should be no more problem.

Although, it is not so much a problem now with LCD monitors.