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Most definitions say that it is a component of blood that has been in a centrifuge, but I haven't seen any definitions that is associated with sci-fi.

I often came across this word when people talk about something that can be injected into the bloodstream for unusual effects that are beyond what we can do today.

An example would be a serum containing tiny little machines called nanites or nanobots. Some might call it nanosubmarines, but I'm sure they pretty much mean the same thing.

In other uses I have seen, serum was used as a dye, so that certain tissues would be seen and marked for manipulation. I think this exists in real life, but there is also something called truth serum.

• So, what exactly does serum mean in this context?

In real world biology, serum is the clear yellowish fluid left over from blood when you separate out the blood cells, normally by spinning in a centrifuge. It can still contain antibodies among other things, but no red cells.

In recent decades the word has also been misappropriated by elements of the cosmetics industry for use in describing some of their products to give a veneer of scientific authority to them.

there is also something called truth serum

Neither pentathol nor any other drugs with similar effects are a serum in the proper scientific use or definition of the word, despite often being colloquially referred to as a truth serum.

What does the term 'serum' refer to in science fiction stories?

In science fiction it pretty much means whatever the author wants it to (or thinks it does).

In my experience it most often means an injection that bestows long term (or permanent) physical / physiological advantage or improvement of some sort. The "super soldier" serum that made Steve Rogers into Captain America is a prime example.

Their effects often bear closer resemblance to something that might be achieved with gene therapy than anything a real serum can do and take instant or near instant effect from a single injection. This in no way is meant to suggest there is anything remotely realistic about some (or even any?) of their effects, simply that a closer ("closer", not "close") real world analogue for them would be gene therapy rather than the word serum that is most often used for them.

But the effect of a "serum" in science fiction can be anything, so really it defies any definitive definition other than simply saying that it's any sort of handwavium that bestows powers or effects if injected.

Google: serum meaning

Cambridge Dictionary : Serum

Quora : serum in biology

In addition to the other two answers, serum could also be a blind idiot or false friend translation. In German, serum has mutated in common use from the scientific definition via antiserum to become medication in a more general sense.

Compare the use of truth serum in English.

Apart from being part of the blood, "Serum" might also mean medicine that is made from blood.

E.g. Merriam-Webster names as a possible meaning:

medical : serum from an animal's blood that can be added to a person's
blood to prevent or cure disease

From there it's speculation, but it is easy to imagine how this would come to be used as a synonym for any sort of concoction that has active ingredients (as in, "if a serum makes you healthy, why shouldn't a super serum make you better than healthy"). So a serum is (usually) an injection that makes you in some way special (e.g. the "Super Soldier Serum" from Captain America).