What does "X is not a four-letter word" mean?

Solution 1:

Idiomatically a four-letter word is a swearword, considered rude and unacceptable in certain contexts.

The implication is here is that thinking and coming up with original solutions to problems is not to be frowned upon in the same way, and indeed is acceptable and encouraged.

Solution 2:

It simply means "[X] is not a swear word."

The implication is that you have been avoiding [X], and the speaker is assigning a (highly unlikely, as the speaker is well aware) cause to that avoidance. As such, it's a form of hyperbole.

Solution 3:

The phrase "four-letter word" is used to refer to one of the many offensive slang words in the English language containing four letters.

Usually the word fuck is intended or implied but there are many others, as listed by Wikipedia in your link. Again, from your Wikipedia link we learn that other languages have a similar term, sometimes referring to three or five letters depending on the language and its key swear words.

To say something is not a four-letter word is often used humorously or to provoke thought, since the author is suggesting that the something should not be considered especially bad. Often the something isn't commonly thought to be bad at all, hence the mild humour.

Solution 4:

There is a popular song by the band Cake called Friend Is a Four Letter Word on their album Fashion Nugget.

Excerpt:

 But to me, coming from you,
"Friend" is a four-letter word,
"End" is the only part of the word
 That I heard...
 Call me morbid, or absurd,

 But to me, coming from you,
"Friend" is a four-letter word.

(Mostly unrelated, but as the question has already been answered I thought it was an interesting example)