First of all regular expression will allow you to check if a given String (in this case the brand of the item) is within a list.  Which means: on the left side of the condition you will need to select: Item Brand. This will be the String we want to check against the list. In regular expressions, items can be separated by "|" symbols. 

The most common use case for regular expression is when you want to check if the category/ the name or any other cart item parameter is within a list of values.
For example:
In your campaign, you want to give a discount on shoes of the following brands: Nike, Adidas, Puma, and Vans. Without using a regular expression operator you would need to set up 4 different cart item filters to realize that campaign – using the regular expression operator will reduce the number to 1. 
In our case, the regular expression will look like:   Nike|Adidas|Puma|Vans

A good way to test a regular expression is to use this website:  RegExTester
After you've inserted your brands in the "text" area and your expression in the "expression" area the brands will be highlighted (blue background) if everything is fine. 

If you want to make the regular expression case insensitive you need to put "(?i)" in front of the list: