Technically the function of "Include existing groups in polygon groups" is to include any pre-existing group names in the obj file you are exporting. If you do not use this option every group in the saved obj file would be unnamed effectively making it all one group. This is often a bad thing. So unless you have a specific reason not to, always use the "Include existing groups in polygon groups" option.

If you look at an obj file in a text editor, each group is preceded by the letter g followed by the name of the group (if any). Under the 'g' line you will usually find a 'usemtl' line which defines the start of a material zone. More info on the obj format at this URL: http://www.royriggs.com/obj.html

In a figure (cr2) each each group is usually assigned to a separate body part. Each body part has a joint and various joint parameters (collectively these are know as a "bone"), this is what allows the figure to be articulated. So groups are virtually essential to an articulated figure. As materials can be easily assigned to a group, groups also make it easier to assign different materials to different parts of an obj file, irrespective of whether that obj is used in a figure or a prop.

When I export an object I usually place a tick (U.S.=check) in the "Include existing groups..." and "As Morph Target..." boxes, and leave the other boxes blank. If you use the "As Morph Target..." option when exporting, it will ignore any translations rotations or scaling that have been applied to the figure (or prop), and in this respect it will be like you cloned the object directly from the figure's base obj file, except that this option will still preserve the effects of any morphs or magnets that have been applied. Whether or not you use the "As Morph Target..." option, will depend on what you are trying to do. In the accompanying graphic the  head exported with  "As Morph Target..." has loaded centrally and without any rotations, even though the figure it was exported from (on the left) was translated and had rotations applied.

I have never found a use for the "Include body part names..." or "Include figure names..." options. I feel they only add unnecessary complications and are best left blank. I'm not sure exactly what the "Weld body part seams" option does, but in a figure the welding happens in the cr2, so it is unnecessary, and probably undesirable to use this option when the exported obj is for use in a figure.