The "reduced correction" glasses are worn at all times instead of normal "full correction" lenses.
The shortest answer is that they don't work.
Under correcting a prescription means that the full prescription is not given, but rather a few steps in power less myopic, or "less minus, more plus" in optical terminology. The result is that when looking through the lenses distant objects, such as road signs, are slightly more blurred than they could be if the full prescription were given.
The rationale for under correcting vision mostly stems from a belief that a full prescription somehow "weakens" the eye since they "won't have to work so hard". The feeling is that somehow vision must be "exercised" if it is to function correctly. What is overlooked is that they eyes became myopic originally when they had no glasses and were under corrected. If under correcting prevented nearsightedness, no one should be nearsighted to begin with.
A scientific rationale for under correcting could be made based on the idea of peripheral hyperopia driving myopic progression. You can read about peripheral focus in the Definitions menu. The idea would be that under correcting a prescription creates more peripheral myopia than a full correction. This is generally recognized as a positive influence on myopia control and should slow progression. The only problem is that it also allows central myopia since the central myopia is not fully corrected. Central clarity can be a strong inhibitor of myopic progression and wearing an under corrected pair of glasses reduces the chance of obtaining this treatment.
In order to actually test this theory, a study by Chung (2002) under corrected 47 people by approximately .75 units. After two years the study was stopped because the people were getting worse than the fully corrected group. It appears that peripheral myopia may only work in conjunction with central clarity, or there may be other unknown factors at play. Certainly one can not recommend under-correction.
Besides the risk that it won't work for myopia control, under-correction leaves the person more blurred than they could be for critical vision activities such as driving or school..
Under-corrected glasses for myopia have less power in them than is necessary for clear distance vision. Typically this occurs as a person becomes more nearsighted and continues to wear their old glasses.
There is no use for the glasses other than as a back-up if the primary pair breaks or is lost.