For many players, just understanding a few terms can help improve a swing. Let's proceed from the terminology that describes what happens at the moment of impact, back through the full swing. (All terms used here apply to right-handed players; left-handers simply switch directions.)
To be able to strike a golf ball well, a player must be able to hit it ball with a square clubface -- that is, with the face of the club perpendicular (or "square") to the intended target line. (Target line is generally shortened to line.) Instructors speak of the clubhead traveling inside the line -- between the golfer and the line -- or outside the line (so that the line is between the player and the clubhead path). The ideal swing takes the club inside the line (or simply, inside) on the backswing to the top of the swing, returns the clubface to square at impact, and brings the club back inside after impact.
If the clubface is open at impact, or aimed to the right of the line, the ball will fly to the right. If the clubface is shut at the moment of impact, or aimed left of target, the ball will go left to a greater or lesser degree.
Release refers to allowing the clubhead to return to square at impact, in a way which, ideally, conveys the power that has been stored up in the backswing. It's one of the terms in golf which most seems to defy explanation; while in a way it could be argued that the proper release is the very essence of a good golf swing, its nature, let alone its description, is a source of some of the most intense discussion among teaching professionals. In instructional terms it's essentially an action through the ball for which the hands are the agents, and it describes how the clubhead is allowed by the hands to proceed from pre- to post-impact. As Shankland puts it: "it's just releasing the energy, is what it is." (Some players who deliberately fade the ball -- i.e., play a shot from right to left by striking the ball with an open clubface -- claim to be able to "delay" their release. That is, they say they don't permit the clubface to return to square until well past impact, or not at all. However, many teachers doubt such a thing is possible.)
When considering the swing as a whole, instead of just simply the path of the clubhead near and through impact, it's best to think of these terms inside, outside, and of the positions of the shaft at parts of the swing in terms of swing planes.
The swing plane is an imaginary, theoretical depiction of the path of the clubshaft traveling through the swing. (It's also described as a sheet of glass which the toe of the clubhead contacts throughout the backswing or downswing, or as a plane on which the shaft rests throughout the swing.) It is used to characterize the angle of the shaft in relation to the ground: an upright swing plane is closer to perpendicular than a shallow plane. The comparison between upright and shallow is important not only for the sake of comparing different players of varying heights and swings, but of the same player with different clubs (since the use of a longer club dictates a shallower swing). Most vitally, to understand the ideal swing, the notion of swing planes can be used to show what's going wrong in a swing that needs fixing.
Each swing really has two planes: the backswing plane, which is the representation of the shaft's progress from address to the top of the swing, and the downswing plane, which in a proper swing is shallower than the backswing plane, thanks to the action of the body allowing the hands to drop the club "in the slot" to transfer momentum leading to impact. Roughly speaking in a perfect swing, both planes would resemble a pair of plywood boards hinged together along an edge that is lined up on the target line -- though technically two such planes would only connect at some point behind the point of contact. There are infinite reasons why two players of the same height and ability will swing the club along different swing planes from one another, and if something is going systematically wrong with a player's swing, it's the teacher's job to diagnose the problem and prescribe a cure.
The commoner swing faults deserve a lexicon of their own:
When the downswing plane is steeper than the upswing plane the resulting swing is said to be "over the top." Thus when a golfer on the downswing throws the club at the ball from the outside with his shoulders he has gone "over the top"; the cause can be, for example, an excessively shallow or abbreviated backswing. Likewise, if the hands are too high at the top of the swing and the golfer attempts to rush his downward move, if he tries to use his hands and arms or an exaggerated lateral movement to compensate for what he senses is an open clubface, to force the clubface to square by coming into the ball from outside to in -- disaster ensues: depending on where the clubface happens to be pointed at impact, he will hit a slice or a hook. However, when a better player goes over the top, the result is generally a hook (a ball which starts off down the target line or to the right of it and veers left) or a pull hook (a ball which start left and curves further left).
A player is said to have laid off the club when the clubhead at the top of the swing points to the left of the target, instead of at the target. Getting the clubface to square at impact is nigh impossible from this position -- without a forced spinning or severe lateral move in the downswing, the clubface will be open as it meets the ball, resulting in a slice. Conversely, if the club is aimed right of the target at the top of the swing, it is said to have crossed the line, generally thanks to a cupped wrist and/or the right elbow pointing away from the body instead of straight down. The almost inevitable result is a hook, since the club is coming from so far inside.