Pin-up is an art form celebrating idealized female beauty, with an emphasis on innocence and flirtation. The most successful "pin-up girls" have frequently become household names, including (in very-approximate chronological order) Mary Pickford, Mae West, Betty Grable, Lauren Bacall, Brigitte Bardot, Bettie Page, Marilyn Monroe, Twiggy, Raquel Welch and Farrah Fawcett.
When photographers talk about "shooting pin-up", there are several different things they could mean.
Today when photographers talk about "pin-up" they often mean shooting in a style which refers back to the 1940s, 1950s and 1960s -- the golden age of pin-up art. Many are inspired by Bettie Page (the archetypal "bad girl" pin-up model) or by Marilyn Monroe (the archetypial "good girl" of pin-up). Others are inspired by (or even obsessed with) the great "cheesecake" calendar pin-up painters, particularly Alberto Vargas, George Petty, and my personal favorite, Gil Elvgren.
Elvgren's work is particularly influential to many "retro" pin-up photographers and models alike. His paintings, with very few exceptions, were very situational, featuring a playfully flirtatious accident such as the subject's skirt being blown upwards to expose a bit more thigh than would normally be seen, or a girl with a playful "oh no!" expression as she spills ketchup on herself at a picnic. While these types of pin-up are flirtatious, they do not cross the line into nudity. Nudity is almost unheard of in this type of pin-up. (Incidentally, pin-up art in this style almost always includes the entire model in the shot, from head to toe; close-ups don't even really qualify as true pin-up in this genre.)
But sometimes when photographers say "pin-up", they mean other things. Some photographers use the term "pin-up" to refer to a certain pop-culture poster-girl look typified by Farrah Fawcett and Cheryl Tiegs in the 1970s. In this definition of "pin-up", the face comes first: it's all in the sunny smile and the twinkling eyes. This type of pin-up is not limited to full length shots; it can include waist-up photos or even portraits. But certain elements of pop-culture appeal are essential to it -- and like the more retro type of pin-up, it generally remains wholesome and does not include nudity.
Others might be referring to a more alternative look, such as rockabilly style, rock and roll, or "biker girl" style -- all of which often feature tattooing, dark cherry-red lipstick, and a feel that is a bit darker than traditional pin-up. (They also often feature motorcycles or vintage hot rods in the photos.)
Still other photographers when they talk about "pin-up" can mean something more sexual. Sometimes they may be referring to the so-called "Playboy style" (which is more correctly called "centerfold", not "pin-up"). Sometimes they mean something even more explicit than Playboy -- which also is not truly pin-up, but more probably erotica or fetish. The term "pin-up" is often used carelessly to describe nude or erotic photography; this is a misuse of the term. True pinup is sexy, but not sexual. Most of it is flirtatious and somewhat conservative. It can occasionally involve implied nudity, but it very rarely ever depicts nudity openly -- and it is never, ever lewd!
When a photographer approaches you about shooting pin-up, it is very important that you clarify what type of "pin-up" they expect to shoot with you before you agree to a shoot. You wouldn't want to expect to be doing a sweet, flirtatious Marilyn-style shoot but arrive at the shoot finding him expecting you to bare everything! Clear communication beforehand is essential, and be sure that you and the photographer are talking about the same type of pin-up.
By the way, if you skipped all of the links above, you might want to go back and click through them all. It's a treasure trove of images exemplifying what "pin-up" is.