I have taken views of many websites and books about how objects have color and they offer only one explanation: it's because they absorb all other colors and reflect color of only one wavelength and black is so because it absorbs all colored wavelengths of light. But if it absorbs all colored wavelengths then shouldn't it be invisible?
When we say an object is invisible we normally mean light passes straight through it. That means it doesn't reflect any light and it doesn't block any light. Something that is black doesn't reflect any light, but it does block light so we can see it by spotting what it obscures.
For example in astronomy we can't see objects if they are so dark they reflect too little light to detect. However we can detect them if they pass in front of a star and block it. This phenomenon is called occultation.