What is Generally Meant by "No Tennis Shoes" in a Dress Code

I believe there's a useful question in here. While we can't say what "No Tennis Shoes" definitively means for a specific company, it is a phrase with general cultural meaning and connotations that can be usefully talked about, such as in this question:

What is appropriate dress for a "business casual" interview?

So I've edited the question slightly to make it a general one rather than company-specific and I submit that it should now be reopened.