The ACGME (Accreditation Council for Graduate Medical Education) is the nonprofit body that accredits most US residency and fellowship programs and sets the requirements they must meet, including duty hours, supervision and curriculum.
It matters to IMGs because ECFMG Certification is required to enter ACGME-accredited training. When you build a program list in ERAS, you are usually looking at ACGME-accredited programs, and a program's accreditation status affects the board certification that follows.
The ACGME accredits programs, not individual doctors. It is separate from the NRMP, which runs the Match, and from ECFMG, which certifies IMGs. Visa sponsorship and eligibility policies are set by each program, so check their websites. See the ECFMG certification overview.