Yep, exactly that. There are laws that say if you work more than a certain number of hours per week, you're entitled to benefits like pension, paid holiday, etc. Zero hours contracts let companies get away with not providing those, as they'll keep each individual staff member below the required hours, because there's no guarantee of a minimum number of hours in their contract.
It's absolutely atrocious, but the government spins it to make it sound like a benefit by saying you have extra time, you can lead a flexible life. What it means in reality for most people is that they need multiple jobs and still get no benefits that a full time job would provide.