An ideal red filter transmits only red light and absorbs all other colors. In this ideal case, a picture containing red, green, and blue would appear red and black when viewed through a red filter.
A red filter blocks green light and blue light: Only red light can get through to your eyes. The white banana and the yellow peel both reflect some red light, so the whole banana looks red (see below; click to enlarge):
A yellow filter blocks blue light, so only red light and green light can get to your eyes. The white banana and the yellow peel both reflect some green light and some red light. The whole banana looks yellow because green light plus red light mix to make yellow light (see below; click to enlarge):
Here, a magenta filter blocks green light and a cyan filter blocks red light (see below; click to enlarge). Only blue light can pass through to your eyes. The banana looks blue because the white fruit reflects some blue light. But the yellow peel looks black. It reflects no blue light.
Likewise, a pure blue filter transmits only blue light, and a pure green filter transmits only green light. Any color from a picture that is not transmitted by the filter will be absorbed by the filter and will not be seen.
When you view multicolored writing through an ideal red filter, only red light reaches your eyes. Red light comes from both the red letters and the white paper (since white contains all colors). The red letters tend to disappear because they blend right in with the red light from the white paper. Letters that contain no red would appear black. Because most pigments are not perfectly pure, you may notice that more than just the red letters blend in with the background. That is, if a yellow letter reflects red (since yellow light can be made from a combination of red light and green light), the yellow letter would blend in with the background.