A transaction in a security is an agency cross if a broker matches orders between two of its clients directly, rather than through the market.
The broker collects a commission from each client, just as it would if the orders had executed through the market. The broker may be able to save clients the spread charged by market makers.
Agency cross trades are regulated in order to ensure brokers do not favour one customer - in particular to ensure that both customers get fair prices.
It is usual for an agency cross to take place at the current mid-price.