The term exclusive is most often used in reference to a toy (or other item) that was only available at a specific store or venue rather that at standard retail in normal assortments.
While occasionally these are simply already-released toys in new packaging (often as multi-packs at a reduced price), most often they are redecoes. Very rarely, a toy developed for a defunct line will find itself released as an exclusive to a particular retailer, so the company can make back at least some of the development costs that went into it.
Though store exclusives in Transformers date back as far as 1989's K-Mart-only releases of the "Legends" Bumblebee, Grimlock, Jazz and Starscream, the practice saw little use in the US until Kay-Bee stores got its own exclusive mini-line Machine Wars in 1997. Store exclusives tied in directly to the main retail line, however, remained minimal in the following years, with Beast Wars and Beast Machines getting one or two.
The success of the Robots in Disguise series caused a boom for the franchise, resulting in the "big four" chains (Wal*Mart, Toys 'R' Us, Target, and Kay-Bee) each getting their own Transformers available only at their stores. Since then, store-exclusives have persisted and increased in number, though with the creation of the Universe series, most have fallen under that line, even well after the Universe line disappeared from standard retail, and even with toys whose backstories place them quite explicitly in other continuities. To this day, multiple store exclusives are released each year in the US.
In Japan, short-run exclusives are fairly common (or, used to be). There are (or, were) multiple outlets for exclusives; for most larger toys, Takara's e-Hobby online store put up exclusive redecoes and "USA Editions", though other online services got some as well. Many brick-and-mortar stores received very short-run smaller exclusives that were technically given away free, but only to people who bought certain toys (or a certain amount of toys) at the stores on a certain date. Magazine mail-aways remain a popular outlet for exclusive redecos in Japan, though that practice has fallen out of favor in the US.
Convention & club exclusives
Convention exclusives have a more consistant history, starting back in 1994 with BotCon 1994's Generation 2 Breakdown, which had been slated for normal retail release with the rest of the team, but ultimately cancelled. The following year saw the first convention-exclusive toy redecoed specifically for the convention, Nightracer (albeit not to the original specifications).
From then on, each official Transformers convention has had at least one exclusive toy... in fact, as time has gone on, the scale of convention exclusives has only expanded, with multi-toy packs, larger molds, and even retooled items.
In 2005, Fun Publications expanded exclusives by producing toys available only to members of the Transformers' Collectors' Club. While one each year is produced as a "free" incentive for signing up, in 2006 the first separately-purchased exclusive, Astrotrain, was produced based on fan-reaction to an unreleased retail exclusive, with more planned.
God hates you and doesn't want you to have toys.
Aside from that, exclusives for both stores and conventions are incentives to get interested buyers to the stores/shows to make other purchases. While you're here for that Transformer or Star Wars Clonetrooper set that can only be found at this store... hey, Dr Pepper is also four for ten bucks. And look, the new Venture Bros. DVD set is out. Need some paper towels? Tube socks?
For store exclusives, often the chain will request (or in the case of Wal*Mart, demand) an exclusive, perhaps even suggesting (or, again, demanding) a specific price point, should the line be proving popular. Sometimes, Hasbro or Takara may solicit items already in the works as exclusives to stores. (Several toys that had been slated for normal retail release but cancelled in the Universe line, for example, were ultimately released as Target exclusives in 2006).
Convention/club exclusives are a bit different, and involve a lot more work done outside of Hasbro/Takara's offices. The convention organizers themselves write up proposals to the company, including the molds they would like to use, color arrangements, names, any new tools they wish to make, and such. These plans very often change depending on mold availability (sometimes molds are lost, or deteriorated, or are being used for other releases) or plans that Hasbro/Takara have in store for the future. In almost every instance, the convention-exclusive toys would not exist at all if the convention organizers did not request (and pay for) them.