Conjunction is a word that connect words, phrases, or clauses. An example of the conjunctions in English are: and, but, because, etc. ASL has a number of conjunctions, which some of them are similar to English (e.g. BUT, IF) but some others are exclusive to ASL.
The gloss FINISH-conj is one of some ASL conjunctions. Be aware that FINISH has multiple uses in ASL: a verb, a conjunction, and an interjection. This post only discusses the conjunction FINISH.
The conjunction finish in ASL is used to link clauses, usually in chronological sequence. It is equivalent to then or when done.
The ASL conjunctions are usually accompanied with raised eyebrows. (a glossing symbol /\ for raised eyebrows)
today ix-me go-ix1 school-ix1 /\finish/\ go-ix2 food+store /\finihs/\ come-here home.
ASL: /\passport to-apply/\ you need /\#do+/\ pick-up application there #PO /\finish/\ fill-out-everything+++ /\finish/\ send-ix1 passport office ix1 [nod]/\ wait++ (nms) [nod/\] receive-it.
English translation with ASL gloss for the conjunction: To apply for a passport, what you need to do is to pick up an application package at a post office finish complete all necessary paperwork finish send it to the passport office and the passport will be sent to you.
Also see conjunction WRONG
More conjunctions beyond WRONG and FINISH.