1To treat someone to a meal, drink, etc. — to pay for someone else as a treat. Very common in everyday conversation.
今日は俺がおごるから好きなもの頼んで。
It's my treat today, so order whatever you like.
先輩にラーメンをおごってもらった。
My senior treated me to ramen.
誕生日だから何かおごらせてよ。
It's your birthday, so let me treat you to something.
いつもおごってもらってばかりで申し訳ない。
I feel bad that you're always the one treating me.
2To be extravagant; to indulge or splurge. To spend more lavishly than usual on oneself.
たまには自分へのご褒美に少し奢ってもいいんじゃない？
Don't you think it's okay to splurge on yourself once in a while as a reward?
普段は節約しているが、旅行のときだけは奢ることにしている。
I normally save money, but I let myself splurge when traveling.