What would "push to open" mean in the context of this switch?
A switch is able to carry current when it is closed --- that is, when the two contacts are touching. 

If you put the switch in series with a light bulb, for example, the switch needs to be closed to allow current to flow through the light bulb and light it up.

NC stands for normally closed. That means the normal state of the switch is closed, and it will be opened (breaking the circuit) when it is activated (for example, by pushing a button).

So yes, "push to open" is the same as NC. FWIW, "push to open" is not standard EE jargon --- possibly it's more common in some specific sub-field like the industrial controls that seem to be the market for the website you linked to.