While many traits that help an individual also help its group, I take it that "group selection" refers to traits evolving that harm an individual for the benefit of the group.

It's really difficult to get this to work, since the selection pressure at the individual level tends to outweigh the pressure at the group level; every group will eventually produce mutants that don't have the trait; these then come to make up an increasing proportion of the group, since they have higher fitness.

Out discomfort with it is due to this.