For what major events does the merrymaking in Othello give opportunity?
The previous answer is right on the money, Iago takes advantage of the merrymaking (and Cassio's weakness for drink) to set his plan in motion. Another interesting thing to note, however, is how little of the actual "dirty work" Iago does. He only introduces the alcohol; it is Cassio (fully aware of his own weakness) who drinks it. And, when he recounts the events of the brawl to Othello, he need only relay the facts of what has happened. It is worth noting that Cassio is actually responsible for his own downfall, ultimately. So, the stripping of Cassio's office is the main event that the merrymaking provides opportunity for.
What is amazing, when considering the sequence of events regarding Cassio that follow, is that Iago could only hope that it would go so well. Othello strips Cassio of his position, which leads to Cassio (at Iago's instigation) asking Desdemona to help him resume his place, which leads to Desdemona spending most of her onstage time pleading for the man that Othello grows to believe she is having an affair with...and the events continue to build and add on from there.
Well, it's quite a pivotal moment of merrymaking in Act II, scene iii, and one that shows how able Iago is to seize the opportunity to set his horrible plan in motion.
If I'm understanding your question correctly, you're referring to the celebration in Cyprus to celebrate the wedding of Othello and Desdemona and the shipwreck of the Turkish fleet. Essentially, since there will be no war, everyone who has just journeyed to Cyprus has nothing to do but celebrate. This merrymaking, though, sets the stage for some important developments in the play. First, Iago is able to get Michael Cassio drunk, which causes Cassio to fight with Roderigo when Roderigo provokes him. This, in turn, gets Cassio dismissed from his position as Othello's lieutenant. Consequently, Iago advises Cassio to ask Desdemona for her help in getting his position back. At the same time, though, Iago begins to tell Othello that Cassio and Desdemona are having an affair--a lie that eventually leads Othello to plot the murders of Cassio and his beloved wife, Desdemona. Ultimately, the celebration in Act 2 is the perfect scenario for Iago, in that its atmosphere helps to facilitate his evil plan. By Act 3, the play's structural climax has occurred, and the play's tragedy begins to unfold quickly.