Tari(たり、)In this case means something like "it could be". Although what stated before is all correct I'm assuming in this context it is used as it could be.
人がソレに求めるものなんて、様々だ。(Im too lazy to translate this part)
それは例えば、自分の居場所だったり。For example, it could be a place for yourself,
例えば、まだ見ぬ幸せへの憧れだったり。For example, it could be an admiration towards an unseen happiness,
例えば、地図の無いこの旅路の、道標だったり。For example, it could be a landmark to this map less journey,
はたまた、理由なんて詮索するのが無骨な、純真だったり。Or it could be a reason that is rude to pry as it is just an innocent motive,
――自分が自分である為に他人を求め、(The rest im once again too lazy to translate)
自分が幸せである為に他人の幸せを考える。
P.S 例えば、 I'm pretty sure everyone knows this but for future users who don't know, it means for example.