The original Antifaschisitsche Aktion was the name of the Communist bullyboys who fought the Nazi bullyboys. They flourished in the weak Weimar Republic after World War I before the Nazis eventually won and Hitler took over.
In the States Antifa has antecedents in the Weather Underground and the Black Liberation Army. It is an intentionally loosely coupled "affinity group" because experience has shown it makes them less vulnerable to law enforcement takedowns.
Antifa members are likely to have ties to political organizations with Antifa support committees such as the Democratic Socialists of America (DSA), The International Workers of the World (Wobblies), the Revolutionary Communist Party (RCP), or any number of other local and regional radical Left organizations or collectives. Antifa draws resources and recruits from them all.The President is absolutely correct that Antifa is a domestic terror group and should be so designated.
And now, with the successful promulgation of the radical message of America as bastion of white supremacy by presidential candidates, cable news anchors, and generations of tenured professors, Antifa is unlikely to lack for recruits and support—rhetorical or otherwise—any time in the near future.
In all turbulent periods of revolutionary politics, whether the 1930s, 1970s, or today, the ability to project force on the streets to punish enemies is a valuable asset. For the Left today, Antifa is that force.