Prigozhin is angry about the fact his own troops (who is clearly cares about) are being used as cannon fodder for putins Army. This has been brewing for a while with reports of low ammunition and lack of equipment, so he has tried to ask for more resources. Yesterday or the day before there were reports that russia wanted to take control of the wagner group (or at least the russian military did) Prigozhin clearly didn't want this, so decided to demand a meeting with the 2 russian military leaders, I would assume to disucuss the matter, as this didn't happen he went through with the threat of marching on Moscow to get his meeting.
Belarus, leader clearly saw a pending bloodbath, so stepped in to try and de-escalate the situation and broker some sort of agreement, which is the right thing to do.