Learn Italian: Non credo che la corrente finisca qui. - I don't believe the current ends here.

Because the sentence begins with Non credo che (I don't believe that). Verbs expressing belief, personal opinion, or doubt trigger the subjunctive mood in the second part of the sentence. Therefore, the regular present tense finisce changes to the present subjunctive finisca.

How does the -isc- pattern work for the subjunctive of finire?

Just like in the regular present tense where we add the -isc- insert to make finisce (it ends), we must also use it in the present subjunctive. For -ire verbs that take this insert, the singular subjunctive endings are always -isca. This makes the forms for I, you, and he/she/it completely identical.

If the subjunctive forms are identical, how do we know finisca means 'it ends' here?

In the present subjunctive, the forms for io, tu, and lui/lei/Lei are all finisca. We know this is the 'it' form because the subject, la corrente, is explicitly stated right before the verb. If the subject were omitted and the context was ambiguous, you would include a subject pronoun to clarify.

Can corrente refer to electrical current as well as water?

Yes! Without more context, la corrente can mean the flow of a river or ocean, an electrical current (power), or even a strong draft of air.