We've been fixing basement floor cracks for more than two decades, no one knows more than us.
There are three things in life you can be sure of: death, taxes, and if you have concrete it is going to crack, you just don't know when or where.
With basement floor cracks, oftentimes they crack because concrete is like a piece of raw spaghetti, if you have any movement at all it is going to break. If I ask you to only crack a piece of raw spaghetti part way, it is next to impossible. You have the soil under the concrete that is settling, you may have footings and those settle too, which can cause cracks.
Not only do you have settling issues but heavy equipment going down the street or earthquakes (there was one felt in Gardner, MA a few days ago) can also cause cracking. Blasting can cause cracks, or when the concrete is poured it can have too much water, too much wind going on over it, or it can dry too quickly. Oftentimes when they pour concrete floors, by code they are supposed to put a vapor barrier or plastic down. They poke holes in that plastic so the water can penetrate more quickly. This can speed up the time that it takes concrete to cure which can also cause cracking.
You may notice in big box stores, some garages, or even in sidewalks that made with concrete that there are lines every so often. These are expansion joints, or basically controlled cracks. These often help concrete from cracking; not a guarantee, but they help. But, in residential construction they don't often put these expansion joints in.
Those are some of the reasons that concrete cracks in basement floors. But, while cracks are unsightly and can cause homeowners concern, most often they are not structural issue. But, basement floor cracks do let a lot of cold air and organic odors up, they also let moisture and radon up. Also, if you want to sell your house, buyers get nervous about basement cracks.
To repair a crack we have to clean it out and sometimes we have to put a specialty sand or gravel down to where the ground is under the concrete because there can be a 3" gap between the soil and the concrete because that material has compacted over-time. So we bring the sand up to the bottom of the floor and then we put a hybrid 2-part epoxy material or a urethane type material into it which actually welds the concrete together and helps stop the moisture, air, or odors from coming in; and it looks a lot better too.