Short answers, pulled from the story.
Encirclement is the situation in which a military force is isolated and surrounded by enemy forces, cutting it off from supplies and reinforcements. The encircled force must either be relieved from outside, break out, or face the choice of fighting to the death or surrendering.
The double pincer is the main form of encirclement, executed by simultaneous attacks on both flanks of an enemy position. Mobile forces such as cavalry, tanks, or armoured personnel carriers drive through the flanks and join behind the enemy to complete the surrounding ring. The encirclement of the German Sixth Army at Stalingrad in 1942 is a classic example.
Sun Tzu argued that a completely surrounded army, with no hope of escape, would fight with heightened resolve and determination, making it more dangerous to defeat. Leaving a gap gives the trapped force the idea that retreat is possible; once they attempt to escape, they can be pursued and destroyed at much lower cost to the attacker.
Motti is a Finnish encirclement tactic used during the Winter War against the Soviet Union. Finnish forces immobilised, segmented, surrounded, and destroyed Soviet columns that were many times larger in number, exploiting terrain advantages to turn the logic of encirclement against a numerically superior attacker.
A siege is a special form of encirclement in which the trapped force holds a fortified position with long-lasting supplies and strong defences, allowing it to resist attacks for extended periods. Sieges have occurred in almost all eras of warfare, while standard encirclement typically involves mobile forces in open terrain.
An encircling force risks being cut off from its own logistical base as it stretches its lines around the enemy. If the encircled force holds firm or maintains a supply route, the encircler can be thrown into confusion or destroyed. Historical examples include Rommel's Dash to the Wire in 1941, the Demyansk Pocket in 1942, and the Burma campaign in 1944.