I just read a guardian article:
Jeremy Deller's artworks draw links between Victorian factories and zero-hours contracts
What are "zero-hours contracts"?
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Zero hour contracts are where you have an employment contract with a company, and thus are required to work when needed. However, you have no guaranteed weekly hours at all, so you can end up working 48 hours one week and none the next.
They have been on the rise in the UK over the past few years for various professions, including ambulance personnel and shop workers. There is basically no upside for the employee, but loads of upside for the employer.
If the employer doesn't need you one week, you don't get paid, but you have to be available if they do want you to work. Otherwise you can be in breach of your contract, so you can't run two or three or these contracts side by side just in case.
A zero hours contract is one that doesn't gaurantee particular hours of work. It just provides a framework for what the employee's responsibilities will be, how much they will be paid per hour etc.
Legally at least in the UK a zero hours contract goes both ways, the Employer doesn't gaurantee work and the Employee doesn't gaurantee availability or exclusivity. https://www.gov.uk/contract-types-and-employer-responsibilities/zero-hour-contracts
The problem is that especially for low-level jobs (which tends to be where such contracts are mainly used) the balance of power strongly favors the employer. Sure in theory the employee can refuse shifts, either because of personal reasons or because they are working with more than one employer but in practice the employer is likely to replace them with someone more reliable. You are left with people who are theoretically "in work" but find it impossible to pull together enough hours to make a living income.
Essentially it's a casual arrangement - you contract to be available within certain parameters, but the employer only calls you in when there is actual work to be done. There is no guarantee of any specific number of hours (and therefore no guarantee of pay).