Q:

What does 'touch' mean in "It opened at a touch"?

Clay promptly withdrew again and hurried across to the window. It opened at a touch and gave on to a wide courtyard. 

A:

The window opened very easily. Clay needed barely to touch it, and it opened. 
The meaning is most likely not literal. Clay might've made a more comprehensive movement than just a single touch to open the window; but that is irrelevant for this narrative; the author needed to stress the fact that it opened easily.   
From the grammar standpoint, touch is a noun, a singular countable noun, as evidenced by the use of the indefinite article a.  "The window opened at one touch", or "at a single touch".

Compare with the expression at a glance:

At a glance: (idiomatic) Upon cursory examination; an abbreviated review. "At a glance it seems that he is a nice guy, but upon digging deeper the truth emerges."

A:

The word touch is a very common word used as a verb or noun.
In the sentence presented, it's a countable noun that means a light movement or placement of a part of your body, specially your hand  on the window.
The window opened only on a light movement of a part of your body, most probably  your hand, and it provided a view of a wide courtyard.

