Why do bee keepers smoke their bees?

Because they can't afford cigarettes.

Sorry about that.

I have been asked a few times why bee keepers smoke their bees and it is part of the bee keeping stereotype for bee keepers to be dressed up like something from Ghostbusters, puffing huge  clouds of smoke at their bees.

The reason its done is that it calms bees down and works in two ways.
Honey bees are forest dwelling animals and to them smoke signifies fire which means they need to get away quickly.
As is the case when they are swarming they might not be getting any honey for a while so they fill up their honey stomachs and they quickly leave the top of the frames to get some honey.
They increase in size by about a third and become quite drowsy.
When they frames are taken out they can be seen, heads in the comb slurping it up.

The other reason is to do with pheromones which are chemical substances they secrete and which act as a communication system for the bees.
If the hive is being opened, or attacked as they see it, they issue an attack pheromone, which triggers their defence response.
If there is smoke around the pheromone is harder to detect and they become less defensive.

Its tempting to use smoke as a bit of a 'cosh' to keep them quiet. I don't have any particularly difficult bees so try not to use too much smoke. Once I had some bees that I called the Bedford Bastards who were so defensive I was often tempted to use a flame thrower on them.

If I am doing something quick or non interventional like checking feeders, I will do this without smoke. A bee keepers truism is 'know your bees'. and if you have defensive bees or have to do something when the weather is unhelpful, then I don't see any reason to be brave and will use some smoke.
For some reason generally the bees at Scald End seem calmer than the Ravensden bees and recently I inspected all the SE bees without wearing gloves and used minimal smoke.