In the play, the concept of "higher love" is based on misguided ideals of war and masculinity.
In the first act, Raina initially voices her doubts about Sergius' ability to excel in combat. She questions whether Sergius' dashing nobility is just an act and whether reading too much Byron and Pushkin has affected her ability to distinguish between reality and fiction. When her mother, Catherine, informs her of Sergius' supposedly brilliant cavalry charge against the Serbians, Raina collapses into Catherine's arms with suffused emotion. She maintains "that the world is really a glorious world for women who can see its glory and men who can act its romance!"
Later, Bluntschli disabuses her of the notion that her fiance had acted wisely. He mercilessly caricatures Sergius as a foolish idealist, a "regular handsome fellow, with flashing eyes and lovely moustache, shouting a war-cry and charging like Don Quixote at the windmills." According to Bluntschli, Sergius acted like an "operatic tenor" on some theatrical stage. The Swiss professional soldier maintains that Sergius almost got the whole Bulgarian side slaughtered. If the Serbian side hadn't been given the wrong cartridges, they would have cut down the entire Bulgarian advance without mercy. As it is, Sergius and his cavalry were only spared because of a technical error on the Serbians' part.
With his comments, Bluntschli helps Raina to understand that her misguided notions about "higher love" are based on vague, indefinable ideas about valor and warfare. While Raina and Sergius' higher love is based on nothing more than Arthurian notions of chivalry, the reality of war is much more grim. Bluntschli relates the difference between new and more experienced soldiers. He maintains that "You can tell the young ones by their wildness and their slashing," but the older ones know that war is about being maimed, killed, and tortured. Bluntschli admits that he hasn't slept in 36 hours, and after almost three days under fire, he's as nervous as a mouse.
Meanwhile, Sergius thinks of war as a "tournament," where he accomplishes great exploits under the inspiration of an adoring feminine admirer.
SERGIUS. Dearest, all my deeds have been yours. You inspired me. I have gone through the war like a knight in a tournament with his lady looking on at him!
RAINA. And you have never been absent from my thoughts for a moment. (Very solemnly.)
Sergius: I think we two have found the higher love. When I think of you, I feel that I could never do a base deed, or think an ignoble thought.
SERGIUS. My lady, and my saint! (Clasping her reverently.)
RAINA (returning his embrace). My lord and my g—
SERGIUS. Sh—sh! Let me be the worshipper, dear. You little know how unworthy even the best man is of a girl's pure passion!
So, from the above exchange, we can see that Raina and Sergius are romantic idealists who are together only because they share the same misguided notions about valor and war. Thus, the "higher love" they share is an illusion.