The name "hybrid" comes from genetics to denote a mixture of two different species with desirable characteristics of both, and the term here has been generalized, combining the familiar swing mechanics of an iron with the more forgiving nature and better distance of a wood.
[1] For many players, long irons (numbers 1-4) are difficult to hit well even with modern clubfaces, due to the low trajectory and very small face of the low-loft clubhead.
The long shaft of a fairway wood also requires much room to swing, making it unsuitable for tighter lies such as "punching" out from underneath trees.
[1] A hybrid generally features a head very similar to a fairway wood; hollow steel or titanium with a shallow, slightly convex face.
The face incorporates the "trampoline" effect common to most modern woods, in which the clubface deforms slightly, then returns to its previous shape, increasing the impulse applied to the ball at launch.
This increased backspin is different from both the iron and the wood of the same number, and creates a flight path similar to a higher-loft iron but at a lower angle of launch; the backspinning ball will lift itself in the air along its flight line, "stall" when the lift generated by the spin coupled with the ball's momentum can no longer keep it in the air, and drop relatively sharply onto the turf.
The sharp drop coupled with the continuing backspin creates "bite"; the ball's forward momentum will be arrested sharply at its point of impact and carry only a few yards thereafter.
By assuming the player's typical putting stance and grip, a ball can be "bumped" in the air over the taller rough onto the green, where it will then "run" (roll) like a putt.