When productivity increases in some jobs, their associated salaries tend to increase as well. In competition for workers, employers also increase salaries for jobs that haven't seen similar productivity increases. As a result, costs of production rise in industries with low productivity growth.
A couple of important expected effects over time, in relative terms:
Baumol himself didn't believe that this would lead to things getting less affordable, because the increased costs are driven in the first place by economic growth - that is, the economy grows at least as much as costs increase. This makes sense to me if and only if the wealth gains resuting from economic growth are evenly distributed, which they plainly are not.