RegEx is a way to parse string, capture some parts and redispatch or replace them in a new string.
Fallout4translator uses the standard syntaxe for regEx. It's a bit hard to understand at first, but it's really powerful.
There are many tutorial over the internet So I wont explain here the syntax of regex, but how you can use regex in fallout4translator 
For the very basics, you can check this: http://regexone.com/ or http://www.zytrax.com/tech/web/regex.htm. (If you know better tutorials, please put them in comments)


To understand the idea, let's take an example: the mod Don't Call Me Settler

It contains a long list of strings like this:
Somerville Place->Oberland Station
Somerville Place->The Slog
County Crossing->Boston Airport
...
each string is separated in 2 parts separated by '->'
1=Somerville Place
2=Oberland Station 

Translating this could be a real pain by hand, but using RegEx is an easy way to get those parts and translate them separately automatically.
If you have that mod, open it in fallout4 translator, select a line that uses this format then go to menu ->tool ->RegEx Translation tool

You get a windows:

• Shows the selected string and the result of the regex you try to use. You can test the RegEx here.
• There you can enter the regEx itself. If you modify it, the sample in 1 is updated dynamically.  Each captured string is stored in direct order 1,2,3... 
• There you enter the replace string.  By using the reference %1, %2, %3... you call call back the strings captured in 2)
• RegExMode:
  -Search and translate: All captured strings are translated if possible then replaced in the format defined in 3)
  -Search and replace: change the format and order of given captured parts
• Heuristic Threshold: when using search and translated, it's possible to use the heuristic translation. Very low threshold is recommanded . In 0.9.8c+, the heuristic option can be define directly in backreference calls (see below)
• If no translation are found, check here if you want to totally reset the new format (if relevant) or keep it.
• Check here which string you cant to change.
• When checked, strings with <Alias> are ignored
  
  

• -Perfect match + direct Translation are in blue
• -Heuristic match are in Pink + yellow light bubble
• -RegEx Match but at least one part wasn't translated are in pink + orange  light bubble (if no parts have been translated you can invalidate the string and reset its state by checking 6)