Black hole is essentially the last stage of the life cycle of a massive star. It is a region in space where it absorbs all matters in its horizon and prevent it from escaping. Even light cannot escape a black hole thus making it hard for the scientist to spot one. But their existence it seen due to physical manifestation around them such as swirling of gas clouds that emits high forms of radiation.
Actually, stars with masses similar that to our sun do not form into black holes. Instead, as the sun ages they will just strip of their outer layer that will eventually form a white dwarf.
But if in the case the sun will be compressed enough to be a black hole, still it cannot suck the earth because it cannot exert a gravitational force greater that what it can do now.