In traditional fund dealing, an investor wires cash, the administrator matches it to an order days later, and units are issued after reconciliation. In the interval, the investor's money is in the fund but their holding is not recorded. Atomic settlement collapses that sequence into a single recorded event on the register.
The practical results are same-day confirmation, no unmatched cash, and a register that is always current, which is what allows daily dealing without a large operations team.