What is the purpose of the USING parameter in SQL?
In the context of your query, USING helps satisfy a JOIN so long as the two tables involved in the JOIN have the same column names to join with. It is like doing a NATURAL JOIN.

Your query

SELECT * FROM foo LEFT JOIN bar USING ('bar_id') WHERE foo_id = 1


works the same as 

SELECT * FROM foo LEFT JOIN bar ON foo.bar_id = bar.bar_id WHERE foo_id = 1


According to the MySQL Documentation on JOIN syntax


  The USING(column_list) clause names a list of columns that must exist in both tables. If tables a and b both contain columns c1, c2, and c3, the following join compares corresponding columns from the two tables:

a LEFT JOIN b USING (c1,c2,c3)

  
  The NATURAL [LEFT] JOIN of two tables is defined to be semantically equivalent to an INNER JOIN or a LEFT JOIN with a USING clause that names all columns that exist in both tables.