Stock market hours are from 9:30am - 4pm US Eastern Time, Monday - Friday, excluding some holidays (check out the full list of “market holidays” here). You can still place orders to buy or sell stock while the market is closed – those orders will be completed when the market re-opens.
It’s important to know that even when market is closed, the world spins on! News and trading can still happen “After-hours”, meaning that the price of a stock can be different at market close one day than it is at market open the next. This is especially important when it comes to pending orders, since a stock you’ve placed an order for after the market has closed could cost more than you have in your Public account when the market re-opens.
For more information on the history of Market Hours check out this article.
There's quite a bit of information behind this, so check out our Guide to Understanding Stock Prices to learn more.