Well...first of all, you do not have to know this.
You pretty much just have to know the chemistry of it (as well as it's structure which is linked to the chemistry), what it is used for, it's environmental problems (pollution, or none, etc) and impact on society (these ones enabled portable devices so very high impact) and cost.
But in my opinion, dry cells may be phased out as new technology comes along as they are quite inefficient for their size (quite big but only like 1.5V). The button cells, especially silver oxide are good because they have a nice steady, constant output which is good for pacemakers and hearing aids, etc. But yeah, lithium ion is the battery of the near future and the stuff we haven't yet discovered will of course be...discovered.
But yeah, you can tell this is pretty much just syllabus stuff as it has sort of been drilled into my brain and changed my opinion^^ ha ha.