When do you use Dictionaries vs using an array?

That's a good general rule of thumb. A dictionary is basically, well... a dictionary--items are associated by key-value pairs and could be returned in any order. That is, accessing the first item in a dictionary might not be what you expect it to be.

Dictionaries are best used in cases where you look up one value to find another (or multiple values) associated with it. Some good examples are given in the Swift course, such as having a dictionary listing country codes with their associated country. Ex:

let countryCodes = ["US": "United States", 
                                  "KR": "South Korea", 
                                  "GB": "Great Britain", 
                                  "IN": "India"]

You might use the "US" country code in one part of your application, but need the full country name elsewhere in the app. You can use the dictionary to look up one value or the other and return the other part of the pair.