An application for security for costs is where you are seeking an order which requires a party to pay money into court (or otherwise) as security for their opponent’s costs of litigation. It tends to be used in circumstances where a party is impecunious or is based outside the jurisdiction and therefore there are concerns about the other party being able to pay costs which may be awarded against them.
For explanations of further keywords & phrases used in the context of commercial disputes we’ve produced a Legal Jargon Buster.