Now like I said, I'm not a tech person, so my stories have little beyond the basic tech of horse and cart, and normal things. No computers or tablets, but you don't really need those things if you have a magic spellbook with an unlimited number of pages. :p But, not everyone is like me, nor does everyone write the same types of stories as I do, so I'll briefly explain (because I don't really know that much) the tech options that I see most of the time. Starting with Biotech.
Now biotech is just what the word means. Tech, obviously means technology, and Bio is Latin for life, so biotech is "living technology." Now how you merge the two is what I think matters the most to a story.
Biotech can be anything, but is basically a machine of some sort made up completely or partially of living cells/parts. In some stories I've read, the biotech is completely biological. They literally grow a computer/ship/whatever by manipulating the base cells into what is wanted. This can get very complicated and starts going into complicated Cellular and Molecular Biology to understand. Thankfully, for writing a story you can leave the science in the background and just do the cool stuff. :D
The most common biotech that I've read is where the machine is only partially made up of living cells/tissue. This is the more simple of the biotechs that can be described. You have the mechanical part of a computer/ship/whatever that works just like a normal machine, but for it to work properly you have to add some sort of living tissue/cells. The simplest idea is hooking a living brain up to a series of wires and it can run a machine or becomes the central processor of a computer. Another simple example would be an artificial limb that can hook up to the central nervous system of the body and work just like a normal arm/leg. A more complicated version of this type of biotech would be when the ship is made up of a non-living body, but the space between the panels; the circuits, circuit boards, and wires; are all made up of living tissue and cells. If the ship is ever damaged, the outside can be fixed rather easily, but the inside has to "heal" just like a living person would.