This is a good read, but the most important bit is this: Robinhood is able to offer commission free trading because they essentially skim money off of every trade you make. This is called frontrunning. It's complicated, but essentially they (via third party market makers) will execute your trades at a little above (or below) the best price and then pocket the difference.
This is a crime, and they've been caught and fined in the past, but how else are they going to make money?
Since many people here are excited about the Gamestop fiasco (everyone is making money now, but even more people will be badly hurt when this is all over) I thought it would be good to emphasize this.
To reiterate ROBINHOOD STEALS FROM THE POOR AND GIVES TO THE RICH
The wealthy hedge fund investors that Re getting pwned right now are getting multibillion dollar bailouts, that's not going to happen to unlucky retail investors when this is all over.
The problem is that they "charge a fee". They mislead you into thinking the service is free, while surreptitiously extracting money from you in amounts and ways that are never made clear.
They only barely make trading more accessible anyway, they just have a slicker app.
Robinhood massively impacted accessibility to the stock market for normal people, who are you trying to fool here?
Sincerely asking: what did Robinhood do to make the stock market more accessible for normal people?