An isosurface is a surface connecting points of equal value. In the context of the CT/MRI lobster scan, the isosurface is a surface of constant density. This is appropriate because it allows the user to inspect the density of the lobster by examining the regions (surfaces) where it is constant. This is the same method by which elevation contours can show a hilly countryside.
There are several advantages to using isosurfaces. First, they are fully three dimensional, and so can provide a good deal of spatial context.
However, the disadvantages are numerous. As the surface is opaque (yet infinitesimally thin), internal structure is often lost, and thus is better suited to monotonic data, where all the points inside the (assumed closed) isosurface have values larger (or smaller) than that on the surface. An alternative is to cut away some of the surface to reveal internal structure, including the possibility of other internal isosurfaces.
Isosurfaces can be difficult or misleading to interpret. It is likely that the isosurface of the lobster will look like a lobster, especially towards the outside. The user needs to be careful to remember that this is a surface of constant density, not any real surface within the lobster.
Further, isosurfaces can be difficult to colour meaningfully. Colouring based on the density is mostly fruitless, as it results in a monochromatic colouring of the surface. However, some other variable may be coloured on the isosurface. The danger here is that the surface may then become too cluttered and hard to comprehend.