The word "conjure" derives from the Latin con- (with) and iutare (an oath), and originally  meant to accomplish something by the uttering of a sacred oath. 

But by Shakespeare’s time the word conjure had taken on a very specific meaning:  to make a devil or spirit appear by summoning it with a sacred name. 

The example with which you may be familiar is a seance where a group sits around a table attempting to conjure up the spirit of someone who’s passed to the other side.

Belief in seances was surprisingly common all the way up to the beginning of the 20th century. Even President Lincoln’s wife organized seances in the White House in an attempt to communicate with a deceased son.

Here, Mercutio jokingly attempts to conjure up the spirit of the love-sick Romeo.

I call on you madman, passion, lover, speak to us; show yourself in the form of a sigh

Of course, asking the spirit to appear in the form of a sigh is absurd since a sigh is invisible, being just a sound.