Hangings are an essential part to good swordsmanship, and mastering them is fundamental.
Hangings, or Hengen in German are an integral part of Historical European Swordsmanship, and have some equivalent in nearly every other style of armed combat I've seen.
To use a Hengen, rather than cutting directly to your opponent with maximum reach, or into what we call Langenort or longpoint, you cut into a position with the strong of you blade off to a diagonal with your point aimed at the opponent's face or throat. You should do this initial cut or Vorschlag from thrusting distance as well.
Cutting this way is counter intuitive at first, since the natural tendency is to cut directly at the opponent, but a dedicated initial attack is dangerous since an opponent who recognizes what you are doing will quickly counter you.
There are two main advantages to using the Hengen:
Cutting into a Hengen controls your opponent as you attack.
If you cut into a Hengen from thrusting range, an opponent cannot simply displace your cut and hit you, since you should by definition be out of cutting range.
Since your strong will already be off to the side and high or low, they cannot cut you successfully from that diagonal, and allows you to quickly adapt high or low to intercept their weak while you maintain your point on the centerline.
This give you the initiate and allows you to control the pace of the fight, which is essential to good swordsmanship.
This also means that they are prevented from rushing in until they deal with your point. This advantage will usually either lead to a fight from the bind, a Krieg, or they will attempt to strike your point which leads to an empty displacement and an opening for you to attack if you are prepared for it.
You can strike suddenly from a Hengen.
The real hidden power of the Hengen is that it threatens an attack done in the time of the hand. By that I mean you can straighten your arm without stepping, reaching your point into Langenort and thrusting your opponent to the face or throat.
This requires that you control the distance of your cut in a disciplined manner, and will require practice until you know the spacing instinctively.
If the opponent deflects your point before this thrust is possible, you are still in a good position to adapt to them as well. From here you can easily do Winden, or other cuts or slices against them that would be too slow from Langenort. Another problem is that from a full reach most would require drawing your blade back, causing an opening for a Nachreisen.