The Select tool is perhaps the most frequently-used tool in MeshEditor. Many tasks can only be accomplished with carefully constructed selections, so it is worth spending the time to learn the ins and outs of this tool.
The main panel is shown below. At the top you can toggle between Brush and Lasso mode - see info about the Surface Lasso mode below. Most of the time, you will use the Brush mode, where you will be "painting" a set of selected faces.
The Filters panel includes controls for a few different extra features of the Select Tool. The first is the Expand Mode. This mode expands/contracts the existing selection, using different criteria. You apply this tool by interactively right-click-dragging, with the Ctrl or Command key held.
The default mode is Geodesic Distance, which means the selection tries to expand by a constant distance across the surface. This is useful for adding/removing a buffer to the current selection. The Crease Angle mode grows the selection across edges where the angle between the two triangles is below the crease angle. This is useful mainly for quickly selecting nearly flat regions. Finally the Vertex Color Similarity mode uses the model's Vertex Colors, and grows the selection to connected regions with a color that is within some threshold from the selected colors.
The Allow Back Faces checkbox allows the brush to be applied when over the back side of surfaces, the areas with the stripe pattern. Normally we do not allow this as it makes it difficult to select around holes. If you accidentally slip off the edge of the hole, you can end up selecting on the other side of the model.
Finally, the Crease Angle Thresh slider, when non-zero, specifies the maximum crease angle that the selection will grow over. So, when it is small, the brush can select over all but the sharpest creases; when it is large, the brush will only add faces that are nearly coplanar with the face under the cursor. Note that the face under the cursor is always added, regardless of this setting.