IMO they server as symbolic constants. Something akin to enums from C if you will.
For example, instead of passing around a magical number of 42, we could pass around :meaning_of_life, and convert to integer at the system boundaries, as @michalmuskala explained here just a few minutes ago.
Other examples include tagged tuples (e.g. {:ok, value}, {:error, reason}, reply tuples in behaviours, etc. If atoms didn’t exist, we’d either have to pass magical integers or strings.
Since atoms represent “well known” pieces of information, they are also used in structs or maps as keys representing fields we expect in them.
If you mean the cost of typing, there was some helper library for that (I can’t remember which one though, maybe someone can step in). Otherwise it’s not really hard to write a simple one converter yourself.
