To be; to exist (for animate beings). Used as a humble/polite or dialectal form (corresponding to いる).
私は会議室におります。
I am in the meeting room.
子どもが庭におるよ（関西弁）。
A child is in the yard (Kansai dialect).
長年この町におる。
I've been in this town for many years.
Auxiliary verb attached to the -te form to indicate a continuing action (equivalent to ~te iru).
彼は今ご飯を食べておる。
He is eating now.
先生は黒板の前に立っておられます（丁寧）。
The teacher is standing in front of the blackboard.
まだ宿題をやっておるよ。
I'm still doing my homework.
Auxiliary verb indicating a resultant or continuing state after an action (the resultant state equivalent to ~te iru).
窓が開いておるから、閉めてください。
The window is open, so please close it.
壊れておる自転車を直しているところだ。
I'm repairing the bike that is broken.
Added after the masu-stem of a verb to express contempt or disdain toward someone's action (similar nuance to やがる). Often colloquial or archaic.
いい気になりおるな、若造め。
You're getting carried away, you upstart.
人の物を勝手に取っておるとは許さん。
I won't allow you to take other people's things like that!