Commenting in a recent Washington Post article — about whether earthworms whose heads are severed from their tails really can and do grow back their missing halves — Mark Zoran, who studies nervous system regeneration at Texas A&M, made the following statement: “[Severed red wiggler tails especially] have trouble mounting productive head regeneration and thus die of starvation and brainlessness, if you will.” As I see it, his use of the expression “if you will” is slightly ironic or mildly facetious: he’s clearly playing on the word brainlessness, which is usually meant figuratively but in this case can be taken more literally; he’s drawing our attention to his hesitant choice of word, and asking the reader to accept it in this context, perhaps with a touch of humor.
“If you will” is an expression that you won’t hear in England, but it is common on the other side of the Atlantic (and is thought by many to be pretentious or fuddy-duddy, especially if it’s used habitually). The British phrase “if you want” is probably the nearest equivalent (but used less often), and is more or less a translation of “if you will”, since will is used here in the archaic sense of “want” or “wish”, rather than the future form of a verb (as in “if you will do something”). Probably more common in British-English are the phrases “as it were” or “so to speak”, which convey a similar sense of word-choice hesitancy, and can also be perceived as pompous, pretentious or old-fashioned.
Geoffrey Pullum on Language Log claims that the expression serves the same purpose as the now ubiquitous discourse particle like: as “a way to signal hedging about vocabulary choice — a momentary uncertainty about whether the adjacent expression is exactly the right form of words or not.” (Although I would argue that this is giving like too much credit; I think of it more as a sentence filler such as er or um, with no discernible intention of meaning.)
The OED explains “if you will” as being “sometimes used parenthetically to qualify a word or phrase: = ‘if you wish it to be so called’, ‘if you choose or prefer to call it so.’” It claims that there are citations of the exact phrase going back to the 16th century, and similar elliptical uses date back to Old English.
According to UsingEnglish.com, “if you will” is used to make a concession in a sentence, allowing the writer or speaker not to commit to a particular argument or assertion, but letting the reader or listener draw that conclusion if he so wishes. It gives the following example: “He wasn’t a very honest person, a liar if you will,” whereby the writer, while not accusing the subject of the sentence of being a liar, allows her reader to draw that conclusion nevertheless.