Here's a fake trip to illustrate the point of rigs:

0815 Show Time
UA 4335 0900-1030 ORD-BNA
UA 3451 2030-2200 BNA-ORD
2215 Release time

This has you working a 14 hour duty day, and getting 3 hours of actual flying. You are literally sitting in the airport for 10 hours and getting nothing for it at an airline without rigs or min day pay. Based on the duty rig for this day trip at AW you would get 7 hours of pay for this day because you take your total duty day (14 hours) and divide by 2 to get the duty rig (7 hours).

This isn't a normal trip because they don't want to pay you 7 hours for 3 hours of flying. But rigs are an insurance policy against exactly this kind of abuse and especially on reserve this kind of thing does happen. (By the way you would get a hotel on this 10 hour sit at AW because it is required by our contract even though you are on duty the whole time)

The trip rig works in the same way except you take your total time away from base and divide it by 4.

Suppose this trip was a 2 day now:

0815 Show Time 5/1/2018
UA 4335 0900-1030 ORD-BNA
1045 Release

Hilton Garden Inn Hotel BNA

1945 Show Time 5/2/2018
UA 3451 2030-2200 BNA-ORD
2215 Release time (a day later)

Now you have a trip with a 38 hour time away from base. Divide that by 4 and you get 9.5 hours (your trip rig). So this 2 day trip now pays 9.5 hours for 3 hours of flying.

If you picked up this 2 day on your days off and it was labelled critical you now get paid 19 hours for 3 hours of flying since critical time is paid at 200% at Air Wisconsin. At first year FO pay of $35 that's somewhere in the neighborhood of $220 per flight hour.

This is an extreme case, but I think it shows you why people talk about rigs so much.