Fundamentals
Guarding the edge between an organisation's own network and the outside world, and trusting what is already inside.
Formal
A security model that places its main controls, such as a firewall and VPN, at the border of the internal network. Traffic is checked on the way in or out, while users and machines inside the border are largely trusted by default.
In plain English
A castle with thick walls and one guarded gate - once you are past the gate, you can walk into almost any room.
In practice
A municipality lets every office PC reach every server freely because they all sit behind the firewall, so one infected laptop brought in by an employee can reach the payroll system.
Why it matters
With cloud services and remote work there is no longer one clear edge to guard, and an attacker who gets inside meets little resistance.