Hand polishes are applied and removed by hand, rather than by machine.
A professional car detailer might use a combination product to hand polish and wax a car at the same time, but these days, they are more likely to suggest machine polishing the car and coating it with a car paint protection product such as a ceramic coating.
However, in the process of machine polishing a car, there might be areas which are difficult for a machine polisher to get to, and so they might hand polish certain areas.
Most of the products that the retail customer has access to in a motor accessory shop will be designed to be applied by hand because the manufacturers know that most customers do not have access to a machine polisher (although, companies like Halford's sell inexpensive polishing machines which are okay for application of retail products). These are good products which work well, especially combination products, however, there are other ways to maintain your car's paintwork, and having a modern semi-permanent sealant can cut out the need for polishing all together.