The AFL-CIO is a Federation of Unions. Individual Unions belong to the Federation (Plumbers - Electricians - Musicians - Nurses - Government workers - full list of AFL-CIO Affiliates here http://www.aflcio.org/About/AFL-CIO-Unions ) . Affiliation is by choice - the members of a Union vote to affiliate - or not. They can vote to dis-affiliate also, as the Longshore Workers have just done.
Over the years, there have been dis-affiliations and re-affiliations. Some unions have never affiliated. One that many DUers might remember - the union that took over the door/window factory to keep it from being shut down a few years ago - is UE (United Electrical Workers http://www.ueunion.org/ ). UE tends to be more progressive/radical by most measures than the unions of the AFL-CIO. (I am a great admirer of UE - though I am myself a member of a union which does belong to the AFL-CIO.)
The purpose of affiliating in a Federation is to make concerted action possible, to build power, to have a mechanism to (theoretically - it doesn't always work) to prevent members from poaching each others' members or stealing each others' work.
The AFL-CIO is not the only Federation. It is itself the merger of two Federations: the American Federation of Labor & the Congress of Industrial Organizations. Currently, we also have "Change to Win" in the US, which includes SEIU (Service Workers).
Some unions left the AFL-CIO to form CtW, some of those have since returned to AFL-CIO - as I said, member unions have that choice.
The AFL-CIO has a checkered history in terms of what we would call "Progressive" actions - VERY checkered. Look up Lane Kirkland, who Fudnick below mentions.
Like any huge Federation there are tensions. Decisions at the top of AFL-CIO have to be more or less consensus decisions among the leadership of the member unions.
There is a fair amount of unrest always, and much of it currently is over the AFL-CIO's concentration on electoral politics rather than direct actions and what many of us consider an over-deference to the current Administration. But of course many others are completely content with that, and many more members don't care - they pay their dues and go to sleep.
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