The big carriers like Verizon and AT&T are officially known as mobile network operators (MNOs). They're the businesses that control all the infrastructure involved in making cell connections happen, like towers and radio access networks. In contrast, MVNOs are "virtual" because they run a network without owning any of what powers it. These companies lease huge amounts of access from the network operators, then sell it to customers at lower rates.
This means when you subscribe to an MVNO like Mint Mobile, you're still on the network that company rents from (in Mint's case, T-Mobile). Direct customers get priority when the network is busy, so its MVNO subscribers might see slowdowns during congestion.
Most of these services are prepaid (service is charged upfront monthly or yearly) instead of postpaid (after each month's usage) like the big carriers. Traditionally, postpaid plans locked you into a contract, but this is no longer common. Instead, they promote "free" phones that are covered by bill credits over 24 to 36 months. If you leave before the device is paid off, you have to cover the balance. Credit checks are also required for postpaid plans.
Aside from not worrying about network ownership, MVNOs keep costs down in other ways. Many of them lack physical stores; support is on the phone or online. If you finance a phone purchase, it goes through services like Affirm instead of the carrier. And they rarely offer bundled subscriptions like streaming services with your plan. Keeping it simple makes business easier for the MVNO and means you pay less as a customer.