How does the hash variable syntax work in typescript?

TypeScript Walkthrough: Interfaces

See the section "Describing an Indexable Object". This is called an index signature.

The syntax for defining the index is:

[Identifier: KeyType]: ValueType

KeyType can be either string or number.

You could claim that the Identifier isn't really needed since it doesn't get used anywhere, but I think it's required in order to force the class/interface designer to indicate what the hash map key should represent (an id, name, e-mail address, etc.). This also provides the possibility of having intellisense show the hash key name (as Visual Studio does for other languages), though I don't think Typescript intellisense currently provides this.

Regarding your question of why the syntax isn't simpler, specifically something like blah:{string:SimpleLayer}:

Because this would be ambiguous. This syntax already exists and has meaning:

var x: { string: SimpleLayer }

This declares a variable x. The type of x has one property, named string, which is of type SimpleLayer. If I wanted to use x, I would do this:

x.string = new SimpleLayer;

It's more obvious if we use a real example:

var circle: {radius: number}

This declares a variable with one property (radius) that is of type number, it does not declare a hash mapping radius types to number types.