To Get Loose
To Escape, To Be Released
intransitive verb, ichidan verb
Remember how 放す is "to release"? Now you're learning the intransitive version. Instead of you doing the releasing, something gets released or freed. So this is to get loose, to escape, or to be released.
放れる describes something held in place coming loose and starting to move, like an animal breaking free from its tether or an arrow being released from a bowstring. You know this because it's pretty rare (れる) for something that's restrained to break free from its bonds. Escaping isn't easy, so it only happens on rare occasions.
The reading is the same one you learned with 放す. If you can remember that word, you can apply the reading over here as well.
風船が女の子の手から放れた。
The balloon escaped from the girl's hands.
あの犬はどうやってクサリから放れることができたんだろう。
I wonder how that dog was able to get off its leash.
息子が私たちの手から放れたら、アメリカに住むつもりです。
Once our son is off our hands, we are planning to live in the U.S.