The lockup period is what it sounds like — a timeframe where shares cannot be sold on public markets. It's not a requirement for initial public offerings, but most new issues will carry some form of the lockup period, generally between 90 and 180 days. But the IPO lockup period should really be considered an insider lockup period since only shares acquired before public trading began are subjected to it.
For example, if you log into your brokerage account and buy shares of a newly-listed company on a public exchange, you don't have a lockup on your shares. You can buy and sell as freely as you wish on public exchanges. But if you requested and acquired your shares before they were listed on public exchanges, you might have restrictions on when you can sell.
The lockup period usually hits institutional investors like hedge funds or asset managers (along with company employees going public) instead of individual or retail investors. Retail traders often don't have access to upcoming IPO shares before they hit public exchanges, so most institutions possess shares. The stock's prospectus must disclose any lockup period before going public.
Additionally, there could be different lockup lengths for different types of investors. For example, a company might decide to release executives and employees from a lockup period at a certain date, followed by hedge funds and venture capitalists at a later date.