Self-intersections:

Trim: When faces to offset intersect together, this option allows to trim unnecessary parts.

Repair: When faces to offset intersect together, this option allows to delete and replace them by faces like fill hole.

 

Surface to thicken 

Thickening with the trim option

 

In green the surface to thicken, in yellow the offset surface.

 

Repair degeneracies : In some cases, boundaries edges of the offset faces become vertices. They can be repaired with this option.