Single switches that control a light are called single pole.
When there are two switches that both can turn a light on or off, they are called three way. (I am not sure about the origin of this label, perhaps because it required three wires; it does not mean that there are three or more switches - those are called four way!) In those switches, flipping the on off control on either switch will change its state: if it was off, it will go on, and vice versa.
When a dimmer control is part of a three way setup, one switch usually controls both the level and on/off, while the other switch only controls on and off. Both switches need to be the three way type.
It sounds like someone has put a single pole switch in a system that needs two three ways. Part of the problem is that there needs to be the right wiring between the switches. There has to be two hot wires*. There also may need to be a neutral wire, depending on the wiring configuration.
To determine the solution, we need to know what the wires are in each box that holds the switches, and what wires are currently attached to the switches.
SUPPLEMENT
It is possible to place dimmers at multiple locations if you use certain digitally controlled dimmers. You still need wiring between the dimmers that are able to have two hot lines, called followers, as well as a ground wire. You also need to provide a neutral wire to the fixture. That sometimes is part of the cable that goes through the dimmer boxes, but not necessarily.
You would appear to have the lights connected to BOTH the dimmer and the fan switch. Presumably this means that things are not really wired the way they were before. You'll need to figure out where this happened and correct it; it's difficult to speculate from afar, but when you get beyond what you can sort out yourself, call in a pro.
Best Answer
For standard switches, that is true. Only one of the switches can be a dimmer (it needs to be a 3-way type) and the other switches are conventional on/off 3- way and 4-way switches. Each of the non-dimming switches turn the lights on at the level set by the dimmer switch. But to change level, you need to go to the dimmer.
There are more sophisticated systems that use a master and slaves. In these systems, each switch can turn on and off the lights at a preset level, or they can override that setting and each control brightness. These switches need to be a matched set, require neutral wires as well as hot, and cost a good bit more than conventional.