Q:

What mean type `a -> m b` in Haskell?

Example - function runKleisli from Haskell base module
newtype Kleisli m a b = Kleisli { runKleisli :: a -> m b }

That means runKleisli have 1 argument with type a and must return function m, which have 1 argument b?

A:

It means m is a type of kind * -> *; that is, m is a type constructor that accepts a single argument, like Maybe or Either String. When you instantiate Kleisli and perform the substitution yourself, you can see how this works out.
For example, consider something like Kleisli Maybe String Integer. The substituted type of runKleisli would be String -> Maybe Integer, and you can see how the m is being used as a type constructor.
For more information about kinds in Haskell, see What exactly is the kind "*" in Haskell?.

