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 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).
Some uses of steering mean any blend of edging and pivoting used by skiers1 to make the skis go around a turn, basically whenever the skis are neither purely pivoted nor purely carved.
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 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.
While these notions are used in many contexts, the main difference between the notions of pivoting and steering is that pivoting is a way to begin a turn and perhaps complete it, with a flatter ski, while steering is something you add to an existing turn, to cause the skis to turn quicker. Pivoting 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).
Pivoting is also a stronger movement to rotate the skis while steering is a more subtle and not as strong "guiding" of the skis.
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, 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 thus any effort to guide the skis around the turn, above and beyond that 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.
See Steering and coiling for a more detailed discussion.
There is a concept of a brushed carve. The difference from steering is that when brushing, the guiding or steering 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, do 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.
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.
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:
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:
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.
A similar but more effortful is to steer 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.
Stivoting is a technique encountered in racing, when the skier comes in "too hot" and has to redirect the skis at the top of the turn.
Pivoting is another version, usually taught to beginners, when the skis are not edged much at all and the skier is instructed to just twist the legs and make them turn that way.
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.