Barre chord

A barre chord is a chord where the left-hand index finger presses flat across several strings at the same fret, acting like a movable capo. That index finger replaces the nut: a chord shape that was normally played with open strings can then slide anywhere on the neck, keeping the same relative shape. That's what makes a barre chord movable: one memorised shape is enough to play the same chord type in all 12 keys.

A nuance few resources explain: only 2 of the 5 shapes are truly barred

The CAGED system presents five open chord shapes (C, A, G, E, D) as five possible barre shapes. In practice, only the E and A shapes (the ones behind the F and B chords) are actually played as a full 6-string barre: the C, G and D shapes require such a finger stretch that they're almost never used as-is on the neck. That's exactly why Guitarshelf's CAGED tool only shows a full diagram for those two shapes, and simply marks the position for the other three.

The "barre chords" sheet category logically focuses on the E and A shapes.