A midpoint order is invisible to the lit book and executes only when a counterparty is willing to trade at the middle of the nbbo. Both sides save half the bid-ask-spread, which is why dark venues and alternative-trading-systems route so much flow there.
The cost is uncertainty: no queue you can see, no guarantee of a fill, and exposure to adverse-selection if the mid you are resting at is about to become stale.
Example: quote 10.00 / 10.04. A midpoint buy for 5,000 rests at 10.02. A seller crosses and you save two cents versus paying the ask, or $100 on 5,000 shares. If the quote is 10.00 / 10.01, the mid is 10.005 and you pay a half-cent, which requires sub-penny-capable venues.
Related: pegged-order, nbbo, hidden-order