an auxiliary verb indicating the passive voice (〜saru/〜される) — marks that the subject receives an action (including the 'suffering passive').
彼は先生に叱られた。
He was scolded by the teacher.
誰かに自転車を盗まれたので、すぐに警察に連絡した。
My bicycle was stolen by someone, so I immediately contacted the police.
その件については社長に説明されるだろう。
That matter will probably be explained to (by) the president. (passive / polite)
an auxiliary indicating potential (ability/can) — for ichidan and certain verbs uses 〜られる (見る→見られる, 食べる→食べられる). For godan verbs potential normally uses -eru (書ける), though colloquial forms using -れる may appear.
この本は図書館で借りられる。
This book can be borrowed at the library.
窓から遠くの山がよく見られる。
You can clearly see the distant mountains from the window.
（口語）あのレストランの寿司は食べれるよ。
(colloquial) You can eat the sushi at that restaurant. (note: 食べれる is colloquial/nonstandard in some contexts)
an auxiliary indicating spontaneous occurrence — expresses that something happens naturally or spontaneously (e.g., 'it comes to mind'). This use can overlap with passive in some contexts.
古い歌がふと心に思い出される。
An old song suddenly comes to mind.
その光景を見ると自然と涙がこぼれてくるのが感じられる。
When I see that scene, I can feel tears naturally welling up.
an auxiliary used for honorific/respectful language — marks respect toward another person's actions (e.g., 来られる as honorific). It has no imperative form.
社長が午後2時に来られます。
The president will come at 2 p.m. (honorific)
先生がこの論文をご覧になられる予定です。
The teacher is scheduled to look over this paper. (honorific; note double honorific forms occur)
お客様がお帰りになられました。
The customer has left. (honorific)