Over defined sketches are those with more relations and dimensions than are needed for the sketch elements to be fully fixed. This is not a recommended status to have for a sketch. Over defined sketches occur when we apply more relations and/or more dimensions than are needed to define the sketch or part of it. To illustrate this, we can add an extra dimension to L2. Once we do that, we will get the following message:

Let's examine these two options and their results:

• Make this dimension driven: This will make the dimension so that it's just for show. This option will only tell us the length of the line. If the lengths of the other lines change, the displayed length here will change accordingly. Choosing this option will not cause any issues.
• Leave this dimension driving: This will give the dimension driving power, just like the other dimensions. However, since the sketch is fully defined already, selecting this option will leave our sketch with conflicting items and a warning message that the sketch is Over Defined, as shown in the following screenshot. Once we are in an over defined sketch situation, we will need to delete some existing relations or dimensions to get rid of the over defined status. In SOLIDWORKS, we shouldn't set more than one relation or dimension that governs the same sketch entity, even if they are geometrically non-conflicting:

Keep in mind that the best practice is to have our sketches fully defined to ensure that we are fully capturing the design intent of our sketch. 

All the definition statuses are related to how many relations and dimensions we add to our sketch. A fully defined sketch has all the sketch elements fully fixed with the proper amount of relations and dimensions to fully capture the design's intent. Under defined sketches have fewer relations than they require, and over defined sketches have more relations than needed.