Who was Maes Hughes?

Maes Hughes was Roy Mustang's closest friend and the most enthusiastic family man in any anime — perpetually showing photos of his wife Gracia and daughter Elicia to anyone in range. He was also one of the most perceptive intelligence officers in Amestris, which is why he died.

What was their friendship like?

The most functional adult male friendship in the series. They supported each other practically and emotionally — Hughes quietly enabling Mustang's political ambitions, Mustang trusting Hughes with the parts of himself he couldn't show subordinates. They argued, understood each other, and needed each other in ways they didn't perform publicly.

How did Hughes die?

Hughes discovered evidence of the conspiracy at the heart of Amestrian government — specifically the homunculi's involvement in central command. He was murdered by Envy (in disguise) before he could report it. His death was staged as suicide. He died in a phone booth.

How does Mustang respond to Hughes' death?

Publicly: stoic. He maintains composure through the funeral, through his subordinates' grief, through the investigation. Privately: Hawkeye finds him in his office in the rain, soaked, having stood at Hughes' grave. The rain on his face is ambiguous — Mustang says he cannot find the source of the moisture. It is the closest he comes to crying publicly.

Why does this scene matter?

Because it demonstrates the emotional cost of Mustang's chosen mask. He has decided to become the kind of person who doesn't weep publicly — because public grief is political vulnerability. Maintaining that mask in his worst moment is the most expensive thing he does. The scene is perfect precisely because it shows the cost without naming it.