On paper, that means you don't have to join the union in order to get a job - just pay the union fees and work under the union contract (which is to say, almost all the downsides of joining but without any actual say in how the union is run). In practice, I think people who do this tend to get blacklisted by the union and have trouble getting jobs in future. I know the Hollywood unions in particular are very aggressive and public about threatening anyone who takes that option with blacklisting, and there are zero consequences for them for doing this.
The law bans employers from requiring people to be union members before they are hired. In states without right to work laws it is still legal to require employees to join the union after being hired.
I've no idea why the US unions tend to be closed-shop, possibly because the high antagonism from employers makes it the only stable solution.