what exactly does a consulting firm do?

like IBM or SiM

In short, they have some highly developed internal models that they apply to problems/projects that their clients approach them with. They employ subject matter experts in the fields that they service who can provide practical advice based on relevant experience, backed up by "the math" behind the solutions coming from their proven models/frameworks.

Many companies don't have deep experience in certain areas or the bandwidth to handle certain projects, so rather than try to hire on people and go through all of the trouble to develop that experience they short cut the process by hiring consultants. Sometimes, however, folks will hire consultants to simply provide them with cover/approval for things they want to get done at the company. For example, if a project fails, the executive can lean back on the fact that IBM thought it would work as well and perhaps that saves their job/reputation.