to make someone laugh; to crack up (laugh a lot)
“A quoi bon se retenir si on a envie de se désopiler, de crier son amour, de le sublimer par le verbe et par le geste, cet instant-là où tout paraît beau où toutes les « interférences » idéologiques et religieuses se noient dans les flots de sentiments passionnels et profonds.” — What’s the use of holding back if you have the desire to cheer up, to shout your love, to elevate it through words and actions, that moment when everything seems beautiful, where all ideological and religious ‘interferences’ drown in the currents of passionate and profound feelings.
From “désopiler la rate” or “to unblock the spleen.” Such a blockage was once presumed to cause irritability (see splenetic). From the Old French désopiler, from des- + opiler (“to block”).