This explanation from Anthem Blue Cross is the best one I have seen:
The U.S. Office of Personnel Management (OPM) Multi-State Plan Program (MSPP) was recently established under the Affordable Care Act. It directs the OPM to contract with health insurance carriers to offer at least two plans (one at the silver level and one at the gold level) in each local exchange. The MSPP is intended to promote competition in the Marketplace and help ensure consumers have more high-quality, affordable health insurance options. All MSPP plans will include “a Multi-State Plan” at the end of their name when listed on the exchange - this designates it as an OPM-sponsored plans. It does NOTmean that consumers selecting the plan will have health plan coverage in multiple states.
Select silver and gold level Individual plans that our company currently offers have been designated as OPM-sponsored MSPP plan options in every local exchange, except Ohio and Connecticut. These plans will include “a Multi-State Plan” at the end of their name when listed on the exchanges. We want to clarify that the required “a Multi-State Plan” designation does NOT mean that consumers selecting the plan will have health plan coverage in multiple states
So, the Multi State Plans (MSP) are plans of same design, benefits and tier level offered by a carrier in multiple states. These are not plan that allow in-network access across state lines.