The new Time field which can be found in the sandbox at the moment enables you to easily add a time to a record. This can be as a manually entered field or as a formula field. People have been finding uses for this in various firms including event control, project management, within cases and for recording appointment dates which can be easily provided to customers.
It is great to see such a long-standing request taking shape in the Salesforce environment but at present it does have a few limitations. These limitations include only being in GMT, not currently being able to be converted to text or number, and not being available in the process builder. However, these limitations can be seen as a good thing at this stage of the beta as it ensures that the base functionality works correctly.
As far as when to use the new field, the rule is to keep it simple at this stage. Personally I have found it very useful for showing client appointment times. This was previously controlled via a complex formula pulling from a time and date field which lead to difficulties for appointments which had more open timeframes such as AM or PM. With the current limitations and possibility that this functionality will not become a production feature it is not worth spending multiple hours configuring, however it is something that you should be aware of as it could easily become a stable of the Salesforce environment. It is a field type which could be very powerful, especially when you consider that fomula functions such as TIMENOW have been enabled already.
I look forward to this being rolled out to production so that the functionality can be fully utilised for customers. If you have any questions about this though then the Success Community is definitely a good place to look.
There are 2 types of Time fields in Winter '18 beta: - as a custom field with Data Type = Time, or - as a Formula field that returns type = Time