Since you say that you are basically mechanical, I will use a mechanical analogy:
You want to do take a precise measurement - say the height of an object. But you have to do it in a high-speed boat bouncing on the waves. Not easy. Vibrations and shocks disturbs the measurement.
If you could install a heavy platform and cushion it on vibration dampers, the task would be a lot easier. No more bumbs and shocks.
An EMI filter works the same way. It filters the bumbs and shocks (transients and high-frequency noise) away and lets the useful signal through.
The useful signal can be something like a TV signal, an analogue temperature measurement - or plain old mains voltage.
In the TV case, your filter has to let rather high frequencies through, at least 5 megahertz (MHz). In the temperature case, a filter with a cut-off frequency around 1 hertz is OK. And in the mains voltage case, everything above 50 or 60 Hz should be filtered away (for practical reasons and cost reasons, a mains filter lets up to a few thousand Hz through).
So, an EMI filter can have many shapes. From a simple capacitor or ferrite bead to multi-section filters with reactors (coils, with or without magnetic core), capacitors and resistors. They are built to let useful frequencies through and block off noise frequencies.
To get back to the mechanical analogy; they are the shock absorbers and mufflers in the electric world.