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On BF exchange it is literally punters laying bet offers for other punters to back.
A non-insignificant portion of Betfair usage is bookies mitigating their risk. As gbj says, modern bookies are a brokerage/arbitrage business, so if there's one outcome of an event with excessive exposure they'll use (amongst other places) exchanges like Betfair to mitigate that risk.
Old school bookies (and some independent bookies still) used to run on the principle of a long term profit due to the overround, and could often be put in a bad spot by couple of unexpected events in quick succession. Modern bookmakers like to run things in a way to make a guaranteed small profit on each event regardless of the outcome (again, much like Betfair).
Greenbank
The.Gren
Nope.
On BF exchange it is literally punters laying bet offers for other punters to back.
No intermediary, algorithmic or otherwise. Just a rake for the service provider.
Contrast this with when a bookie is looking to find an arbitrage they take a risk of not completing it.