It's not possible to have a best Mozart opera, that's just silly, they're all best, but if there was one, this is it. The most perfectly balanced comedy, with the most beautiful music, and the sincerest and most heartfelt passion.
It was first performed in Vienna on 1 May 1786, with libretto by Lorenzo da Ponte, based on the second of three Figaro plays by Pierre de Beaumarchais. (The first was later to be Rossini's The Barber of Seville). The play's title was La Folle Journée, ou Le Mariage de Figaro, and was premiered in 1778. Mozart and da Ponte's opera was in Italian, and the title was Le Nozze di Figaro. In English both that and The Marriage of Figaro are common; recently English National Opera did a version calling it Figaro's Wedding to try and convey the freshness.
The Barber of Seville tells how the barber Figaro aids the wooing and marriage of Count Almaviva to Rosina. When the present opera opens, Rosina is now the Countess, and Figaro is planning his own wedding to the Countess's maid Susanna. Act One opens with Figaro pacing out floor space for their future quarters.
But the Count is still a lecherous old goat, and would like to make Susanna one of his conquests. It would become quite confusing (well this is an opera) to try to list all the romantic attachments and mix-ups that propel this tragi-comedy through its four acts, so, in summary:
Marcellina wants to marry Figaro. Doctor Bartolo the music master helps her. By the end of the opera it is discovered that Figaro is Marcellina and Bartolo's son. -- The spirited young pageboy called Cherubino (a trouser role, i.e. a soprano) loves the Countess, though he'd happily love anyone else. The Countess is sad because her power to keep the love of the Count is waning with age. Her aria at the beginning of Act Two is possibly the most poignant and beautiful in the whole piece. -- Figaro ensnares the Count and exposes him to the Countess by having Susanna agree to an assignation in the garden. -- And so on and so on.