Steering a turn means many things to many skiers and you will likely hear it used in many contexts, but generally, steering refers to making an active effort to guide and torque the skis around a turn, efforts to rotate and point the skis in a different direction, or guide the skis around the turn, very related to pivoting (which means twisting the feet actively, with a flatter ski).
Steering involves an appropriate blend of all four skills, using a stronger focus on leg turning to create slower rounded turn shapes. When steering is done correctly it should leave a 30cm wide track from the beginning to the end of the turn. APSI 2019 Interski Presentation 1
Other definitions describe it more specifically as any blend of edging and pivoting2, but we prefer the definition above.
Since most skis these days are designed to turn once put on edge (via the sidecut), whether they are "carving" or not, steering is often contrasted with carving and most often, steering is used to mean oversteering: and just means any way you can make the skis turn without carving and, since there are many ways to achieve this and to avoid confusion, we consider that as a separate, more generic concept and it has its own topic: Oversteering and we leave steering to mean just actively guiding the skis:
Here is a good video from Josh Foster:
Note that some refer to pivoting as the simple rotation of the feet, without regard to it being active (turning the skis) or passive (following a turning ski) and there is often confusion between separation and pivoting. Let's take a look...
While these notions are used interchangeably in many contexts, the main difference between the notions of pivoting and steering is that pivoting is generally considered a stronger effort of rotating a flatter ski, while steering is a more refined blend of skills, but still has a leg turning component. Pivoting a ski can only happen when the skis are fairly flat on snow, at very small edge angles or when the skis are unweighted and pulled from the snow (like in a hop turn).
This type of turn is common when the skier is on terrain that's too steep for the current skill level or when you have to quickly change the direction of the skis at small speeds (at higher speeds, deflecting the body across the slope requires a more definite edge engagement).
When the ski is turning because of the ski design and snow interaction (let's say more towards the carving spectrum), there is a certain tension in the lower legs, required for the separation of the upper body from the lower body, where the lower body "follows" the skis around a turn and the upper body does not (i.e. coiling or counteraction).
Steering is the active one, so any effort to guide the skis around the turn, above and beyond that passive foot rotation required for separation.
During a high performance transition, where the skis cross under a coiled body, some active resistance in the feet and legs is also required to not allow the body to unwind, although this time this effort is required to not allow the skis to rotate while unweighted, so in a way, directly opposite to steering.
There is a concept of a brushed carve. The difference from steering is that when brushing, the guiding or active foot rotation effort is missing and/or not emphasized. The skier makes the same movements as in a carved turn, except, by managing a smaller edge angle as in a carved turn, the skier does not let the skis engage strongly and the ski will skid somewhat.
Overall, when brushing, the tail follows the tips as it would do in a carved turn, but with more displacement (skid). So brushing differs from steering by not requiring extra rotational input into the skis, using the exact same techniques and movements as carving, but the same simple speed control as skidding the turns offers, with that passive foot rotation we discussed above*.
The pivoting and rotation of the feet can be effective at small angles, with a relatively flat ski that can easily pivot/skid. When the edges are engaged at small angles, steering is more related to creating and maintaining separation and coiling through turning the legs in the hip sockets than to guiding the skis forcefully, see Femur rotation.
When the ski edges are well engaged, at high edge angles, a pivoting effort would want to lift the tails and disengage the edges, but in reality, the tails are important in the second part of the turn, in high-performance skiing, so you'll need to be careful to generally avoid that.
...and another good video from Josh Foster:
This is a related concept, defined in relation to the ski's direction in the snow: how much is the ski steered or turned against the direction of travel. Think of it this way: at every point in the turn, if the ski was fully engaged, it would point in a certain direction, which is the tangent to the arc (ignoring the ski bend, to simplify this).
When we do a hockey stop, the steering angle is maximum, or 90 degrees, while when we are carving edge locked, the steering angle is zero. The steering angle can also be explained as the amount of tip and tail displacement from a fully engaged or pure carving position.
The internal femur rotation happens from tipping and edging. The steering angle [...] happens from a forward/backward movement of the leg.Reilly McGlashan, Legacy part 1 1
One other related term is oversteering, i.e. causing a ski to make a shorter turn than the ski design would make otherwise and there are several mechanisms to do just that, besides pivoting and steering:
All these mechanisms can be used on top of the ski design, to shorten a turn, i.e. make the skis come around faster.
To disambiguate the terms, we prefer to call that Oversteering and, as you see, it's not all about steering or pivoting the skis forcefully (i.e. with a rotational input).
A lot of the following steering variations are techniques that were used back in the day of the long straight non-carving skis. Some are used on super steep runs, extreme all mountain carving etc.
Pivoting the skis in conjunction with a hop in transition, so-called hop turns. This is usually seen on very steep terrain.
Pedal turns are also used in the steeps.
Heel pushing is a variant where you push the heels out more forcefully, resulting in an even shorter turn, generally frowned upon as too forceful.
Stivoting is a technique encountered in racing, when the skier comes in "too hot" and has to loose some speed and redirect the skis at the top of the turn.
I am absolutely certain you have already steered many turns and know what this is: the brain finds it very easy to just turn the skis, subconsciously adding some "steering", when it needs to.
Steering allows us to deal with terrain that's beyond our abilities to carve and ski using the ski design or to complement it. In racing, some steering is used, when the required line does not permit the skier to carve arc to arc, but as mentioned above, there are many ways to oversteer the skis and racing is too dynamic to specify just one (i.e. as a forceful rotational input).
One of the big reasons we recommend not relying on steering via pivoting is that it involves many large muscles, which set in motion additional angular momentums that then require attention to control, causes the skis to break snow engagement etc.
Steering is useful when we ski stuff that is beyond our current ability but always seek to control it just with edging, pressure and balance and using the ski design, for better balance.