A call-to-arms is a special diplomatic action that happens in the context of a war.
A vassal may call-to-arms its direct or indirect superiors in a Nation, inviting them to participate in their war.
This participation is optional: the superior will receive an event asking him to answer the call or declined it (note that he event times out as a negative answer by default if the player ignores it).
There is no consequence for declining a call-to-arms.
On the other hand, if the player agrees to it he will immediately enter the war as a co-belligerent, bringing automatically with him all its own vassals as well (as they have the contractual obligation to follow their liege in wars).
Entering a war through a call-to-arms does trigger breaking clauses of Treaties that are active with enemy belligerents in the same way declaring war as the main agressor would.
A war can therefore escalate to involve a whole nation if a Nation leader answers a call-to-arms from one of its vassals.