You display a price and privately authorise a better one. The order sits in the book at the displayed level but will trade up to the discretionary limit when contra flow arrives.
Think of it as an iceberg-order for price rather than size: the market sees a passive buyer at 20.00 and does not see that the buyer will actually pay 20.03.
Example: display a buy at 20.00 with three cents of discretion. Another trader posts an offer at 20.02 inside the spread; your order reaches out and takes it. Anyone reading level-2 to estimate real demand at 20.00 has understated it by three cents per share.
Related: pegged-order, hidden-order, sweep-to-fill