This the is the overall puzzle category, containing every puzzle except the Beginner puzzles with (<15) and (<150) brackets. Doing well in this category means you're well versed in all forms of folding, even if you're not the best in one particular category.
This category contains prediction puzzles. In prediction puzzles, we know which amino acids compose the particular protein, but we don't know how this particular protein folds up in 3D space. Players work to get the highest scores - the higher the score, the more likely that solution is how the protein folds in nature. Knowing how a protein folds up in nature is important because it tells us what role the protein plays.
In this category, players design proteins to create new materials, target problematic molecules in diseases, and enhance existing proteins - among other things. Protein design involves inserting and deleting the amino acids to/from the protein, and also changing which amino acids compose the protein.
Symmetry in proteins refers to what we call oligomers: proteins that use many identical copies of themselves to bind together and form a "symmetric" complex. We call it symmetry because each copy folds the exact same way, and these copies arrange themselves with rotational and/or translational symmetry.
CASP (Critical Assessment of Techniques for Protein Structure Prediction) is a protein structure prediction competition that is held every 2 years, with labs from around the world testing out their newest state-of-the-art folding methods on unpublished structures. CASP ROLL is a "Rolling" CASP, which happens continuously in the time between the main competition. More about CASP ROLL here: http://predictioncenter.org/casproll/
Electron Density puzzles use experimental data to assist players in folding the proteins. The data is the result of X-ray crystallography, and is shown in game as a 'cloud'. Fitting the protein inside of the cloud will increase the likelihood that your fold it correct, and will also increase your points.