There are two main acoustic quirks of indoor rooms that have an impact on how speakers (and instruments, and voices) sound. They result from how the room is shaped, and what the room is made of. Room nodes are one of these quirks, and they result almost exclusively from the shape of the room.
All frequencies of sound move at the same rate: 343m/s (there are various other factors like temperature that can affect this rate, but frequency isn't one of them). But lower frequencies have a longer wavelength -- the fact that they change direction less often means that one cycle of the wave covers a much greater distance.
This fact means that when a room's dimensions are an exact multiple of a wavelength, those waves can build up and cancel each other out (constructive and destructive interference).
As a result, when you hit one of several specific low frequencies indoors, you'll suddenly find that the volume changes a lot depending on where you're sitting in the room. Areas where it is unexpectedly quiet are room nodes, and areas where it is louder than expected are anti-nodes.
As the frequency increases, the wavelength becomes shorter. As this occurs, room nodes will even out more and more, until the interference effect no longer matters. As a result, you don't have to worry about room nodes above about 500Hz (depending on room shape, speaker type, etc).
The exact frequencies that cause nodes depends on the shape of the room. Most rooms in Western buildings are cuboid (rectangular), and calculating the frequencies is fairly straightforward for them. Simply take the dimensions of the room (length, width, height) and apply a simple equation to each:
Frequency (Hz) = (343/2) / Length (meters)
This will provide you with three numbers. These three numbers are the fundamental modes of the room - the frequencies that room nodes will affect the most. All of the multiples of these frequencies -- double, triple, quadruple -- are also likely to have the same issues. And frequencies which show up more than once among those three groups (these are called convergences) will have even bigger problems.
"But wait!" you say, "We've calculated each of the dimensions of the room. But sound waves bounce in all directions, not just straight up-down left-right forwards-backwards!"
You're right. There's another equation for all the nodes that bounce off more than one wall. It's a little more involved so you can find that in another post.
Room nodes are incredibly problematic to fix. The problem is with the actual dimensions and shape of the room, and you can't normally change those.
In an audiophile setting, you may want to invest in bass traps -- devices which counter-resonate at a specific frequency and break up these resonances. But be prepared to be disappointed: you'll have to pay quite a lot of money for modest results.
The reality is that if you really, really need to eliminate bass resonances -- you'll need to use a room constructed with the right dimensions in the first place. You can't eliminate resonances entirely, but you can minimize their impact by choosing dimensions that spread them over the frequency range.
The mathematics of non-rectangular rooms is more complex, and on top of that the equations are different for each room shape. As a result, there's no simple or clear-cut way to predict how an oddly shaped room will respond to bass.
Realistically there are very few situations where you have the ability to change the geometry of your room, and even fewer where the room was constructed with an ear towards resonances in the first place. And the solutions that are available aren't great.