Not quite skimming. When a stock is purchased, there is also a seller. But the buyer and the seller are not usually in direct contact. There is a middle man called a market maker. The market maker actually purchases the stock from the seller and then sell to the buyer. This results in a slight difference between the buy price and the sell price, often called the bid and the ask prices.
Why do this? Because the number of shares being sold rarely match the number of shares being bought for one. But more importantly, if a person wants to sell his shares and there are no current purchasers, then the price of the stock would dramatically drop. So the market maker is legally required to purchase that stock even if he has to hold it for a while. So the job of the market maker is to combine/split purchases into sells AND to provide a high degree of stability to the stock price.
Many brokerage houses provide a similar service for their larger clients. They are generally referred to as institutional investors as opposed to the normal investors often called commercial clients. Institutional investors are often able to make their purchases as a lower cost than commercial clients, but have additional fees, usually based on the amount they are holding in the brokerage house. The idea is that they might only be getting 1% of the account value per year, but that also increases the incentive for the advisors to increase the value of the account. The better the institutional investor does, the more money the broker make.
Since brokerage houses can hold equities and then sell directly to their clients, they can offer investment products which are not available outside of the brokerage house. That’s how most 401Ks work. If your company has a 401K with Fidelity, your 401K may be invested in funds which simply don’t exist outside of Fidelity. When you retire and roll your 401K into a traditional IRA, the funds you had in the 401K will often have to be liquidated and then new purchases in mutual funds and/or ETFs will be purchases inside of the IRA.
So in effect, the brokerage house acts much like a middle man similar to a market maker.
What Robinhood did is totally legal. They purchased x number of shares of stock from a brokerage house and then sold to their users. Their income is based on the margin between those prices. What got them into trouble is not what they did, but rather that they didn’t disclose how they made their profit - and that’s a big no-no in the finance world.