As my van considers starting to be an optional activity I invested in one of those little jump starters. It's about the size of two fag packets, charges from a usb and cost about seventy squids. The reviews were positive but I was still sceptical until I tried it on my unenthusiastic Transit which fired up immediately. I've used it half a dozen times since with similar results. Impressive. So, what magic of electronics goes on inside?
Nothing more complex than a battery capable of putting a couple of amp-hours into the vehicle battery, but very quickly, so hundred or more amps peak current, but hopefully not for long enough to do any damage.
Some of the developments in batteries that have made electric vehicles possible have been those that allow a very low internal resistance, so a very high maximum current is possible from surprisingly small cells The slight downside, is that there are now more battery related fires..