There isn't much really that hasn't already been said about Leslie speakers. An invention of the late 20th century, and featured on countless recordings between the 60s and today, it's a staple of recording in general, let alone organ performances. It's actually inspired countless effects pedals and other simulations. The basic premise is that it is a rotary speaker, one that spins in a cylindrical fashion while running. This produces a really cool, natural sonic effect that is rather cool. It's basically a natural version of the effect that is often referred to as tremolo or sometimes vibrato. Half of the legend of the Hammond organ is a result of the Leslie Speaker, without it, the organ loses much of its character and really doesn't work as well for most sounds.
The debate as to whether to buy a Leslie is different nowadays. Basically, if you own the organ, you need it. It's worthless without one, and getting a good one is important. However, if you are going to make like George Martin or Tom Dowd and pick it apart to hook it up to other instruments, you might consider a vibrato/tremolo effect that mimics it, simply because of the price and labor. It's a very unpractical endeavor with a rather limited payoff, unless of course you are trying to record a big-budget record. Most people wouldn't even consider it. I'll tell you though, it will be hard to find an effect that can truly match the speaker, especially in the studio. So basically, be wise when purchasing, but if you are going to get a Hammond organ (especially a B3), the Leslie Speaker is essential.