Ganderite's synopsis is wonderfully elegant and concise, but I cannot agree with it.
I would explain it as jackets allow a bullet to be more tolerant of high performance or non-ideal conditions. In particular a jacketed bullet will be much more tolerant of poor bullet to bore fit than will a lead bulle (lead bullets must fit the bore closely, if they are undersized accuracy will suffer and accumulation of metal fouling will be atrocious). A jacketed bullet will be more tolerant of a wide range of peak pressures and burning curves than will a lead bullet (lead bullets are notorious for shooting poorly if accelerated quickly by moderate charges of fast powders, such as using Unique in a .40 S&W.) Jacketed bullets can be pushed faster than lead bullets. Jacketed bullets may be used without lubricant, while lead bullets must have some kind of grease- or wax-based lube.
The primary advantage of lead bullets is that they are more economical and they are easy to customize to work well with a specific gun. But the corollary to that is that the user must have the knowledge and patience to do that customizing, or they may not shoot well at all. In that sense, jacketed bullets are plug-and-play, you just buy some and load them up. Making cast bullets work to their best potential becomes a hobby over and above reloading (which is a hobby over and above guns and shooting).
The production of mass volumes of factory ammunition, suitable to give acceptable performance in guns of wide range of manufacturer and vintage, would be much, much more difficult without jacketed bullets. Though of course, that is not what you are trying to do here. The .45 Auto cartridge is inherently low pressure and low velocity, and is a very friendly round to load cast bullets for. It's a very good place to start learning.