There is a public book of buy/sell orders.
HFTs would prefer not to put their orders on these books for various legitimate reasons (including fees).
If (and only if) HFTs (or other trading firms) are willing to offer the user a better price than the best available price on the market, Robin Hood will just give the order to them instead of placing the order on the public market.
So if the market price is $10, and an HFT is willing to sell for $9.95, then Robin Hood might give the user an execution price of $9.97 and keep the 2 cents to themselves.
The user gets a better price than they would have on the open market, and a better price than they were expecting.