A particle attached to the -masu stem of verbs to list actions/examples (as in “doing A and doing B”), used in constructions like “...tari ...tari (suru)” to indicate alternating or repeated actions.
休みの日は映画を見たり、本を読んだりします。
On my days off I do things like watch movies and read books.
子どもたちは公園で走ったり、遊んだりしている。
The children are running and playing in the park (doing things like running and playing).
夏は海に行ったり、山に登ったりします。
In summer I go to the sea, climb mountains, and so on.
An adverbial use after the -masu stem to mean “do such things as …” or “sometimes do …”, often implying occasional or example actions.
彼は会議中に居眠りしたりするから困る。
He sometimes dozes off during meetings, which is a problem.
あの犬は急に吠えたりすることがある。
That dog sometimes suddenly barks (does things like barking).
彼女は急に歌い出したりするから面白い。
She's funny because she sometimes suddenly starts singing.
When repeated after the -masu stem and placed at the sentence end, it can express an imperative or exhortation. This usage is somewhat literary/old-fashioned in modern Japanese.
行きたり戻りたりせよ。
Go and come back! (Imperative; literary/archaic tone)
よく聞きたり覚えたりせよ。
Listen well and remember! (imperative, somewhat formal/old-fashioned)
(Classical) An archaic copular/auxiliary derived from 'to ari', attached after nouns to mean 'to be'. Found in classical Japanese; not used in modern colloquial Japanese.
彼は賢人たり。
He is a wise man. (classical/archaic style)
(Classical) An archaic auxiliary verb, from '〜te ari', attached to the -masu stem to indicate completion or the continuation of a state (similar to '〜てある' in modern Japanese). Found in classical texts.
書きたり物は机の上にあり。
The things written are on the desk. (classical phrasing indicating completed state)