Batteries are used to store extra energy, and are required if you want to use non-laser weapons or even turn and thrust at the same time, as without batteries your generator may not be able to power all your systems at once.
Human batteries come in 6 sizes. The smaller batteries are sold all across Human space, while the largest two are only sold in certain systems in the Deep and Rim. Supercapacitor are tiny, 2-ton batteries that only provide 150 energy. They are more expensive than LP036a batteries (which are 10 tons and give 1000 energy) because of how small they are. Supercapacitors can be placed in that last bit of outfit space that you may have left over, allowing for you to use more of your outfit space for more important outfits.