What is the link between strong vocabulary and good communication skills?

Of course.
We use spoken and written words every single day to communicate ideas, thoughts, and emotions to those around us.
Sometimes we communicate successfully because good vocabulary can help us say what we mean.

Good Vocabulary helps you to express yourself in a better way. So, rather than saying a long sentence and confusing yourself as well as the listener, you can probably shorten the sentence and make it more meaningful using an appropriate word(vocabulary).