The letter k refers to a sub-section of Section 401 of Internal Revenue Code.
In 1978, Congress amended the Internal Revenue Code by adding section 401(k), whereby employees are not taxed on income they choose to receive as deferred compensation rather than direct compensation.
The law went into effect on January 1, 1980, and by 1983 almost half of large firms were either offering a 401(k) plan or considering doing so.