It's just a feature of the matching engine. It's not really that complicated. The venue, let's say BZX, accepts an order from you to display a BID for 100 at 20.01 and you flag the order and tell the matching engine you'll accept 20.015.
When someone comes along and wants to sell, let's say Grandma Sue, she might say: Sell 100 at MARKET. The displayed market is 20.01 / .02. With your bid in the market Grandma will get matched at 20.015, a .005 price improvement over the displayed bid of 20.01. This is a good thing.
It looks like MPL orders are undisplayed. Then how can they "display at a price but execute at a separate price"? Or, what does it mean when I read "The MPL order is an undisplayed limit order that is priced at the midpoint of the Protected Best Bid and Offer (PBBO)" if it doesn't actually mean undisplayed.
There is confusing terminology amongst venues. The key points are: you can execute at the midpoint or at any discretionary offset from the primary or market.
EDIT:
It's just a feature of the matching engine. It's not really that complicated. The venue, let's say BZX, accepts an order from you to display a BID for 100 at 20.01 and you flag the order and tell the matching engine you'll accept 20.015.
When someone comes along and wants to sell, let's say Grandma Sue, she might say: Sell 100 at MARKET. The displayed market is 20.01 / .02. With your bid in the market Grandma will get matched at 20.015, a .005 price improvement over the displayed bid of 20.01. This is a good thing.