When someone in design or engineering refers to 2D CAD, they generally refer to a drawing on a screen or paper that represents a 2 dimensional object or assembly. This means there is no depth represented (Z-axis).
In Order for designers to illustrate a depth they usually add another view alongside the front or side view.
2D drawings are always presented in a line drawing format but may have some shaded view added.
2D CAD drawings are generally produced to give dimensions to a part or assembly for the object to be made or instructions for parts to be assembled.
The reason drawings are produced are so dimensions and tolerances can be added where necessary to ensure parts fit together perfectly.
In manufacturing 3D is generally used to relay information for dies to be made but again 2D cad is required for tolerance purposes. In engineering today 3D is generally used and recognised by many machines, which saves programming times and cost.
In most cases you wont be able to view any files that your designer does unless they save the 2D cad drawings out as a PDF or an image. If you would like to view or edit the drawings yourself you can download very good versions of 2D cad software from companies like Solid Edge.