"大げさ" is a noun that means "to exaggerate". It is used when describing situations in which someone makes something seem larger, more important, better, or worse than it really is.
"話を盛る" is a phrase that has the same meaning with "大げさ", but it is only used to describe situations in which someone makes a story seem larger, more important, better, or worse than it really is.
You may often hear "盛っている" or "盛った" in everyday conversations.
- Leo: Are you okay?
大丈夫? - Ken: I'm okay. It seems that I fainted from anemia.
うん。貧血で倒れたみたい。 - Leo: Lie down until an ambulance arrives!
救急車だ車で、横になっていて! - Ken: What? It's just anemia. You’re blowing it out of proportion.
えっ?ただの貧血だよ。大げさだよ。
- Meg: Do you want to go to ABC restaurant? Their steak is really good. It's bigger than my face and very thick!
ABCレストランに行かない?あそこのステーキ、すごく美味しい。私の顔より大きくて、超分厚いの! - Amy: Really?
そうなの? - Meg: I might be stretching the truth, but it's definitely delicious.
(話を)盛った(or大げさ)かも。でも、本当に美味しいの。
- Meg: You know, it seems like Kumi's boyfriend is kind and so cute. He looks like Park Seo-jun!
ねぇ、クミの彼氏って、優しくて、すごく格好良いらしいよ。パクソジュンみたいだって! - Amy: Are you serious? She was exaggerating a little, right?
本当?(話を)盛っている(or大げさ)でしょ? - Meg: Could be, but she told me that she doesn't think she'll ever meet anyone like him again.
そうかも。でも、彼みたいな(素敵な)人には二度と出会えないだろう、って言ってたよ。 - Meg: I think she made her story sound much more dramatic than it really was. It's too early to say something like that because they've just started dating.
随分大げさ(or話を盛り過ぎ)だなぁ。付き合い始めたばかりなのに、そんな事を言うなんて早いよ。