Because these are not actual static types, you can get a lot of control and say things like "this function accepts three arguments, all integers between 5 and 50, but in increasing order, and the output must be a float between 0 and 1", and then have that checked on the function before the program ever runs. At run time, you can then verify that you are passing in valid arguments.
Spec is relatively new, and there are experiments in the community to do things more like traditional static type checking also. The future is an interesting place.
To statically check constraints like "all integers between 5 and 50", you need dependent types, and Clojure doesn't support this.
Considering this, I'm not sure what you mean by "before the program ever runs". Do you mean a check thanks to automated property-based testing (which is a way of running a part of your program)?
I think the main advantage of a type system (e.g. Java's) is that it avoids a lot of stupid mistakes; and therefore does help refactoring because most "stupid" changes will simply not compile (rename a function but forget it's used in 3 other places? boom)
Static analysis with Spec might be a great booster because it gets you the expressiveness of Spec to static code reasoning.
I've used static and dynamic languages. When using a dynamic language, I usually don't miss static language features, except when refactoring and/or maintaining a large code base. It's the reason why I'm interested by Flow and TypeScript (in the JS ecosystem), mypy (in the Python ecosystem) and even static languages like Go. It's also the reason why I'm a bit reluctant to invest in Clojure, despite being interested by the language.