How do color filters placed in front of a light source,change the color of light that passes through?

What we perceive as colour is basically the frequency, or combination of frequencies, of the light shone on our retinas.

The light that comes out of a light bulb (but, note, not of an LED) is a mixture of lights of many different frequencies, actually, of all frequencies in the visible range. This is what we call "white". Filters have the properties of absorbing certain frequencies: this is due to chemical properties of the molecules of the pigments within. A blue filter absorbs all colours except blue, etc. So yes, the intensity will drop. LED coloured lights do NOT work like that. An LED produces light of a single frequency, so we require different LEDs to make a white-looking lamp.

To determine the colour of a light source in an objective way, without relying on subjective feeling, there are instruments called spectrometres. These can be very precise and are used for astronomy and chemical analysis.

Polarisation is unaffected by a coloured filter, but polarising filters exist.

"Color" is how we sense visible light with different mix of wavelengths. Each wavelength of light in the visible range is a particular color. White light is all the wavelength mixed together at the right balance.

What filters do is attenuate selected wavelengths of light. A red filter blocks most blue light, for example. If you start with white light and take out the blue, green, and some of the yellow, the result looks red.

The reverse also works. You can create white light by combining light of multiple colors at the right proportions. This is how computer displays work. Look at a white area on your monitor with a jeweler's loupe, and you will see individual dots or red, green, and blue. These colors match the color receptors in your eye. This allows a wide range of perceived colors to be created by balancing the relative proportions of the red, green, and blue contributions.