I'll break it down for you:
Buster Moon, owner of the New Moon Theater, made an attempt to get a gig with his cast at the Crystal Theater, owned by Jimmy Crystal.
However, he promised to get someone in the show who's been missing for more that 15 years; Rock legend Clay Calloway.
A few days after they get a room booked at a hotel, Jimmy introduces his daughter, Porsha, who claims to have a dream that Moon asked her to sing for him, eventually snatching the lead role from Rosita, one of Moon's cast members.
After Jimmy finds out that Moon lied about having Clay's permission to use his song, or that he knew Clay personally to begin with, he told Moon, and I quote, "I swear if you didn't have my kid in your show, YOU'D BE OUT OF THAT WINDOW BY NOW!!" , and tells him to get Callaway by the end of the week.
Almost a week later, Moon comes back empty handed. Luckily, Ash, another one of Moon's cast members, stays behind and is able to convince Calloway to come to the show. More about that in a minute.
As Moon gets everyone ready for rehearsal, and Porsha flatly recites her lines, he asks to have a word with her, which results in her thinking he's firing her.
When Jimmy finds out that Moon "fired" her daughter, it spread to the news, he tries to make her stop crying by saying "Will you stop your crying?! You've embarrassed me enough!! Now the whole WORLD thinks I got a talentless loser for a daughter!! Take her home!", which only makes her sob more.
And when Moon tries to explain what happened, Jimmy doesn't listen, grabs him by the collar, and holds him over the balcony.
Long story short, Moon made a promise he couldn't deliver on time, and Jimmy overreacted like the snowflake he is.