Foreign currency nostro is a slightly redundant phrase for what is normally just called a nostro account, and that entry covers how such accounts are opened, funded and used. This page explains why the extra words appear.
A nostro ("ours" in Italian) is an account a bank keeps with another bank, usually a correspondent bank abroad, in the currency of that other bank's country. A UK bank that needs to pay suppliers in yen on behalf of customers might hold a yen nostro with a bank in Tokyo. Because almost every nostro is held in a currency other than the bank's own, specialists rarely add "foreign currency". The phrase is used mostly by treasury and operations staff who want to separate these accounts from domestic clearing accounts or from accounts held in the bank's base currency.
Foreign currency nostros tie up cash, since they must hold enough balance to cover outgoing payments, and they carry exchange-rate exposure that treasury teams manage alongside foreign exchange risk. Each nostro must be matched daily against the bank's own records in a process known as nostro reconciliation. The other side of the relationship, seen from the bank holding the account, is a vostro, explained under nostro, vostro and loro accounts.