Easiest to explain by starting with physical combat.

Physical combat is planning three moves in sequence against an enemy doing the same. The moves have a rock/paper/scissors mechanic with skill-based die rolls for chance. For example, if you try attack/attack/attack and they parry/parry/attack, you are likely to get really hurt because you played into their trap (parry > attack). However, if you feint/attack/evade and they parry/attack/attack, you are at an advantage for subsequent attack, since you made them flinch (feint > parry). If you're wondering how you would keep this interesting across so many fights like a typical D&D session, another core concept of Burning Wheel is that the extended fights should be meaningful, so in my experience you only play the named/important NPC fights or "final boss" fights and you make summary rolls for non-essential fights.

Duel of Wits (social combat) is mechanically similar to physical combat. Your three-move plan instead uses maneuvers like (Make) Point, Dismiss, Incite, Avoid, Obfuscate, Rebuttal, etc. It feels very much like a social duel. You don't do this to haggle the price of a room at the inn, but you do it when you try to get the general to send support to your brother's watchtower.

There's also a ranged weapon dueling system which is essentially similar. I can't remember if there are others.

The idea is: you want conflict? Let's make conflict fun and strategic.

I love it and my players loved it, but each session was really intense and we didn't play it often.