The Offset tool is similar to Extrude, but one thing you will find about Extrude is that if your selection has concavities, fold-overs will be introduced if you push the surface far enough. Offset is a more complex operation, trying to solve for an offset surface at a constant distance that doesn't have foldovers. We do this by incrementally remeshing as we solve the Offset.

If you are doing 3D design in Meshmixer, particularly if you are trying to design things that fit other things, you will find Offset to be fantastically useful. The shortcut combo for Offset is ctrl+d

The property pane for Offset is show on the right. The Distance parameter specifies the offset distance. This can be positive or negative.

The Accuracy parameter controls the precision of the offset-surface solution. This is basically controlling the density of the remeshed offset surface - more triangles means a more consistent offset thickness.

The Regularity setting is also a control on the internal remeshing, essentially it controls the amount of smoothing during each remesh pass. Generally more smoothing means a better solution, however high smoothing can also cause thin or small areas to collapse, and then the Offset solution will be incorrect.

Normally the Offset is a separate surface that we stitch with a tube, very similar to Extrude. However when the Soft Transition slider is non-zero, the behavior is different. In this case we try to "blend" between the original and offset surface. The distance specified by this slider controls the wide of the transition band. The image below shows an example of this, with a standard Offset on the left and a soft-transition offset on the right. This parameter is very useful if you wish to thicken a thin part.

 
 

The Connected checkbox controls whether the Offset surface is stitched to the base surface with a tube (ie like Extrude) or an offset copy of the base surface (like Extract). Note that in Soft Transition mode, this checkbox is ignored.

The Preserve Boundary checkbox only has an effect on non-Connected offsets. When this is un-checked, the boundary is free to move and be remeshed. When checked, the boundary loop is preserved, and its position is defined strictly by normal-vector offsets. Note that for large offset distances this will often cause foldovers & artifacts. 

Finally, Preserve Groups determines whether the input groups are maintained in the Offset surface. If so, they group boundary loops are constraints on the internal remesher, which can reduce the quality of the Offset surface. When this setting is un-checked, each offset surface is assigned a new facegroup.

Tips

The Offset tool with Soft Transition is a good way to Thicken thin parts. However you do want to make sure you start with sufficient triangles. For very thin parts you probably want to do a pass of Remesh in Linear mode, to add subdivisions. In general, because it is based on remeshing, Offset is sensitive to the input triangulation, and low polycounts will trip it up.

Another potential issue is if you have small sliver triangles around the offset boundary. Because we use the surface normal information, the offset surface may end up pushed in undesirable directions. If this happens, remesh around the border to clean it up. We find this happens a lot when using Smooth Boundary to create a nice border loop - because it doesn't remesh, Smooth Boundary will often produce tiny local foldoers. You can use the pattern doubleclick-group-select, expand, doubleclick-group-deselect, expand, expand, to select the ring around the facegroup border. A quick Remesh will usually resolve any problems.