Everything that WS has mentioned is true, although I am afraid she may have confused you in the process. Plus, the rules regarding this have just changed.
1. A medical license is required to practice medicine in the US. Each state gives out it's own license, but the rules are mostly the same. You must pass all 3 steps of the USMLE, and you must have some minimum amount of US training (usually 3 years). All physicians get the same license, regardless of what field they practice. You must have a license to practice
2. Board certification is an administrative process that "proves" that you know the minimum amount about your field to practice it competently. Each different field has a different mechanism for proving board certification. In order to be board certified, you need to complete a US residency/fellowship in that field, and then pass whatever tests they require for certification. You do not need to be Board Certified to practice (but see below).
So, IMG's had two choices. The "best" choice is to come to the US for residency and complete it. This then allows the IMG to be licensed and board certified in that field. But there was a "back door". IMG's could complete a base residency (such as IM, or surgery) in another country. Then, they could come to the US and do a fellowship. In that case, the time spent training in the fellowship counts towards the minimum needed for licensure -- so as long as the fellowship is at least 3 years long, the IMG can be licensed. However, most boards require core certification in order to be certified in the subspecialty -- so the IMG can't be Board Certified.
Problems with this plan:
1. It was very difficult to get a fellowship without completing a core US residency. Possible, but very very difficult.
2. Not being board certified can be a big problem. Some insurance companies won't allow you to be listed on their provider lists without it, many hospitals won't allow you to be on staff, etc. But there are exceptions.
3. Perhaps most importantly, the ACGME just changed the rules. Starting in July 2015, fellowships are ONLY allowed to accept residents who completed ACGME, ACGME-I, or the Canadian equivalent training. There might be exceptions, each RRC can decide for themselves. This rule has two major outcomes -- IMG's will no longer be able to use fellowships as a door to a US license, and DO's who complete an AOA residency will not be able to complete an ACGME fellowship.