The Transform tool is used to Move/Rotate/Scale the selected faces. This is similar to the whole-object Transform tool found under the Edit tab. As the selected faces are moved, we stitch them back to the original mesh with a tube-shaped surface, similar to the Extrude tool. A simple example is shown below, where a circular region is selected, then translated vertically, then rotated and scaled.

The hotkey to start this tool is t. Note that This is the same as the object Transform tool, we resolve the ambiguity by context (if you have an active selection or not)

The property panel for the Face Transform tool is shown to the right. The panel only has a few options which control behaviour of the tool. 

Shared Frame

To understand the Shared Frame option, we first must explain how the 3D transformation axes are determined for the Transform tool. When you have a single selection, we can use the average triangle normal over the selection to define a local frame. This is the default behaviour, as shown in the left image below. The perpendicular axes are arbitrarily assigned. You can alternately toggle to the World frame using the 3D widget, shown on the right (see the Transform Tool page for details)

The Face Transform tool can also be applied to multiple selected areas simultaneously. In this case, we default to the World frame (shown below-middle). However, by un-checking the Shared Frame option, you can transform each selection relative to its own local frame (below-right). Note that only one 3D widget is shown, on one of the selections. The move/rotate/scale you apply to this frame is duplicated relative to the other frames.

One complication with the per-selection frames is that although the Z frame directions (ie the normal-to-surface directions) are reasonably well-defined, the other two axes are somewhat arbitrary for each selection. So, you may find that certain transformations do not transfer in a sensible way to the other frames.

Fixed Boundary

The Fixed Boundary option only applies when your selection contains boundary edges. The default behavior is to move these boundary edges, and hence there is no stitching that happens at boundary edges. When you enable this option, the boundary edges are pinned in place, and as you translate the faces, we stitch back to these original boundary locations.

The example below shows one case, where an entire square is selected. Normally the Face Transform tool will now move this entire square, just like an object transform. With Fixed Boundary enabled, we move the square triangles but stitch back to the original boundary edge locations, as shown in the rightmost image.