Dynamic typing is that thing where you can assign any type to any variable, right?
Why would you want that?
Same reason you want modular functions that you don't need to know the inner workings of in order to use, just how to call them, what they expect as input, and all that other neat stuff abstraction brings.
Dynamic typing means that types aren't checked until runtime; I think it's a prerequisite for ducktyping, which means that types aren't strictly enforced but you'll get runtime errors when you try to call a method that isn't defined for a particular type. I'm not sure which one allows you to suddenly change a variable's type whenever by something like
a = 1
a = 'alpha'
But anyway, the reason you'd want it is so that you no longer have to worry about types. Instead, you trust that everybody who defined a type did their job properly, so that the methods you call are defined as you expect, and that everybody who uses your code does their job properly, so that they don't feed your code objects without the methods you need. Same way that when you write a function, you trust that the functions you use do what the documentation says, and you trust that users of yours will read your documentation, without anybody needing to dig into anybody else's source code. The idea is that you can say, "Okay, I'm not going to write a different function for adding integers than for floats, I'm just going to use exactly the same logic and assume that adding means basically the same thing for either one".
It adds convenience, and reduces the amount of stuff you need to understand in order to make your code function, provided nothing goes wrong. Of course, things always go wrong, and ducktyping can be an absolute nightmare to debug (for example, somebody unwittingly passes a string to your function, which cheerfully says, "Oh, you mean to concatenate these things!" and moves on until something three functions up breaks because how the fuck am I supposed to square root the string 'foobar').
If understanding your code is the hardest part of your job, ducktyping helps. If debugging is the hardest part of your job, it will quite possibly make things worse. At least, that's my understanding of the question.