• You have a (small) subset of Contacts that you want to keep constant communication, or
  
• You need to do a Batch process, like send group emails, or assign calls, and you need a contact list to hold the target contacts.
  

A little more explanation on the second item. A lot of 'group / batch' process on Contacts are initiated from Contact Search Result: For example you can

1. Do a contact search,
   
2. Multiple select in the search result,
3. Do a (Batch) Mail & Print, or do a (Batch) Assign, or do a (Batch) Add/Remove Sales Team
   

But there are times when your intended target contacts are not easily selectable from one straight forward search. In such scenarios, you will want to

1. Create a contact list, 
2. Do a contact search, multiple select search result, and 'Add to List' -> your new contact list
3. Do another search, repeat above
4. Manually add Contacts to list
5. When your contact list is ready, do the (Batch) Mail & Print, or (Batch) Assign from the list.
   

To get started, navigate to Contact -> Lists.