In other words, if the rate of unemployment was low, the rate of inflation was high, and vice versa. At the time, economists concluded that this was a logical outcome of both being influenced by the rate of interest: if interest rates were low, then unemployment would be low and prices would rise, but if interest rates were high then there would be lots of unemployment and workers would not have much money to spend... so prices would go down.
Unfortunately, when economists tried to design policy around this concept they disrupted the smooth relationship. In the years since the 1960's, there has not been a straightforward relationship, and Keynesian economics has had to be drastically revised to a post-Phillips Curve regime.
There is some correlation between inflation and unemployment, but the correlation is much more complicated than originally thought. It is quite possible to have high unemployment and high inflation (i.e., a high "misery index").