Altitude masks - a fitness fad that has largely passed. Even so you still get a few people that train in these, believing that they are getting some performance benefit... They're not.
The idea behind the mask is to restrict oxygen intake to replicate training at higher altitude, in the hope that when the mask is removed you can train harder.
The problem is, the mask doesn't replicate conditions at altitude. The reason athletes train at altitude is because the air pressure is lower, meaning less oxygen is taken in per breath. A training mask will do the same, but only due to the mask restricting breathing, reducing the volume of your breath in general. This is not the same!
There are many reasons as to why workout masks don't work, and breathing restriction is the most important. A restriction of breathing equals a lowering of workout performance, meaning you are unable to create an adequate stimulus to elicit adaptation.
Even if the mask worked as intended, the style of training people perform is often incorrect. People are often seen doing interval style HIIT training whilst wearing the mask - exercise that uses the anaerobic system. Why would you restrict your breathing when performing exercise that uses an energy system that doesn't require oxygen in the first place?
In addition to this, the exposure time most people have to this style of breathing is way too short! 3 x 40 minutes a week isn't anywhere near enough time to experience the benefits that actual altitude training can offer.
Athletes that use altitude training often have to spend extended period of times at altitude training camps in order to increase their red blood cell count, which allows them to carry more oxygen to muscles. When going back to sea levels, increased oxygen carrying capability and more oxygen per breath = increased aerobic performance.
Now training masks can improve some things, such as the strength within the breathing muscles, however this will again not help your athletic performance. Increasing the strength of the breathing muscles can serve some purpose with those that suffer from Chronic Obstructive Pulmonary Disease (COPD).
Additionally, some MMA fighters have noted that they train with masks in order to try and replicate a scenario where their opponent has obstructed their breathing. This is largely psychological, and doesn't really hold any performance benefit.
So to summarise, training with a training mask is often no more than a gimmick, and often an expensive one at that. If you are looking to increase your performance, focus on training correctly, without a mask, and provide your body with the correct stimulus for it to adapt accordingly. Unless you have a weakness within the muscles responsible for breathing muscles, a training mask is of absolutely no use to you!