Used to express that something can happen or is within the realm of possibility. Often used in formal or written contexts. The more colloquial equivalent is ありえる.
See also: あり得る
Such a thing is quite possible.
It is also possible that he will fail.
Alternate kanji spelling using 有.
Compound of あり (continuative form of ある, 'to exist') and 得る (うる, 'to be able to'). Literally 'can exist', extended to mean 'possible'.