Basically, the frequency of a sound is its pitch. Therefore, an A might be 440hz, or 440 cycles per second. However, an A played on a piano sounds different than an A played on a saxophone, which sounds different than an A played on a trumpet, etc. In each case, it is a 440hz note, but the shape of the waveform is different. The different shapes give different tonalities.
One way of looking at sound is called
Fourier synthesis. Essentially, it is possible to break down any wave into a series of sine and cosine waves. When you add all these sine and cosine waves together, the result is the funky-shaped wave.
This applet illustrates how it works.
Here's a more advanced one that will also let you hear the sound (although it's a bit harder to understand).
In general, every plugin you use in Home Studio will use Fourier analysis to work. This means that if you analyze any sound in a spectrum analyzer, you will see sound all through the sound spectrum - due to the way the analyzer works, it breaks the sound down into a bunch of sine waves at various frequencies.
This isn't necessarily a very accurate way of looking at sound, but it is mathematically simple, and is a good approximation. Therefore most current sound equipment uses it, including your equalizer.
This means that you don't use the equalizer to add and remove specific notes - you use it to adjust the "tonality" of sound. The fundamental frequency of a piano ranges from about 30hz to about 4200hz. (Most instruments have much smaller frequency ranges.) But when analyzed via Fourier analysis, each of these notes is broken down into a series of harmonics (also called overtones). As the applets I listed above illustrate, changing the relative volume of the harmonics changes the "character" of the sound. This is what the equalizer does. It cuts or boosts certain frequency ranges. This causes certain overtones to be cut or boosted. This causes it to sound different when all the different components are added back together to form the sound that you hear.
That's why cutting or boosting individual frequency bands with an equalizer results in an overall change to the sound. It doesn't all of a sudden cause, for example, all notes between C3 and A5 to disappear while leaving all the other notes alone, or anything like that. Instead, it is used to improve the palatability of sound, and how it sits with the other instruments. Boosting low-mids causes the sound to get warmer, boomier, fuller, or muddier; boosting high-mids causes sound to get brighter, sharper, crisper but more cutting; etc.
You should NOT try to use an equalizer to restrict each track to a specific range of frequencies. That's not what people mean when they talk about using EQ to "make room in the mix". But music sounds the best when it hits the whole frequency range evenly, not if there are lots of spikes at certain frequencies, with no very little sound at others. A poor frequency spread can make your mix sound muddy, or shrill, or even give you a headache by the end of the song. That's some of what you're listening for and trying to correct when you use EQ.
Be aware that EQ is often best used sparingly, except for the occasional special effects. A good rule of thumb when you are first starting out with EQ is to only use it to cut frequencies, and not to boost. I think it's easier to hear the result of the EQ. Boosting frequencies via EQ is a lot like shouting in order to be heard over the TV - it works, but turning the TV down works better.
It always comes down to using your ears, which takes time and practice. You'll notice that as time goes on, it becomes more and more obvious to you what is clashing in your mix, and what you should do to fix it.