If a transaction is not completed before close of business, the transaction has to be "rolled over" to the following day. There is a danger that changes in interest rates (or currency exchange rates or share prices) could cause gains or losses. Therefore "swaps" are used to avoid losses. The kind of swap is not clear from the context, but it will be some kind of derivative security that will counteract the effect of any loss or gain.

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Note added at 2 hrs (2007-01-28 17:49:03 GMT)
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Actually, reading the question again, it may be that one broker tries to find another broker with a similar "open position" but in the opposite direction and they agree to "swap" transactions. Depending on the prevailing mood after close of business on the way the markets may move overnight, one broker may charge the other a fee.

Or they may use the futures markets, but that's probably more expensive.

SWAP = traditionally, an exchange of one security for another to change the maturities of a bond PORTFOLIO or the quality of the issues in a stock or bond portfolio, or because investment objectives have shifted. Investors with bond portfolio losses often s w a p for other higher-yielding bonds to be able to increase the return on their portfolio and realize tax losses.

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Note added at 1 day36 mins (2007-01-29 16:01:36 GMT)
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Ref.: Barron's Dictionary of Finance and Investment Terms. Fifth Edition. ISBN 0-7641-0790-9