According to http://elixir-lang.org/getting-started/basic-types.html#atoms:
Atoms are constants where their name is their own value. Some other lang
They're basically strings that can easily be tested for equality.
Consider a string. Conceptually, we generally want to think of strings as being equal if they have the same contents. For example, "dog" == "dog" but "dog" != "cat". However, to check the equality of strings, we have to check to see if each letter in one string is equal to the letter in the same position in another string, which means that we have to walk through each element of the string and check each character for equality. This becomes a bit more cumbersome if dealing with Unicode strings and having to consider different ways of composing identical characters (for example, the character é has two representations in UTF-8).
It would be much simpler if we stored identical strings at the same location in memory. Then, checking equality would be a simple pointer or index comparison.
As a consequence of storing identical strings in the same location in memory, we can also store one copy of each unique kind of string regardless of how many times it is used in the program, thus saving some memory for commonly-used strings as well.
At a higher level, using atoms also lets us think of strings the same way we think of other primitive data types like integers.