Biology is often described as the scientific study of life. Which is a pretty good definition, so long as you understand the biological definition of life. What is the biological definition of life? Well, I'm not sure there is one. We are pretty sure humans are alive, as are our individual cells. Plants, fungi, bacteria, these we know are alive. They have cells bounded by membranes. They have genetic material. They grow and reproduce. They exchange gasses with their environment and maintain their internal order by taking in low entropy material and putting out high entropy material.
In high school biology, I was told that viruses are not alive. They are like pieces of paper that say "Photocopy me!" They cause themselves to be replicated, but they don't actually self replicate. They don't grow. They don't exchange gasses. They don't take in low entropy material and put out high entropy material. They don't have a membrane.
Prions, misfolded proteins which cause other similar proteins to misfold in the same way, are even further from the traditional definition than are viruses. Viruses at least have their own genetic material. Prions don't. Therefore, not alive.
But we must be careful about phenomenological definitions. If we define Zebra as "an equid with stripes" then we can make any horse into a zebra by painting stripes on it, and an albino foal born to a zebra mother and zebra father would not a zebra. But an albino zebra is a zebra, and so while stripes are a prominent characteristic of zebrasity they are not a defining one.
So we must be wary of defining things in ways that they have to have some arbitrarily chosen us-like characteristic to qualify. Anthropocentrism is so uncool, and so limiting. Why does life need to have cells bounded by membranes? When earth is invaded by aliens who's tissues don't consist of cells bounded by membranes, are we going to insist that they aren't alive? I hope not. If on Mars we find some manner of critter that self replicates, exchanges gases and takes in low entropy matter/energy in order to maintain a low internal entropy state, but is without genetic material, are we going to say, "damn, we thought we might have life here, too bad?" No. We would say how amazing yet expectable it was that Martian life does it differently than we do.
So I don't quite know what life is, but looking again at that list from my high school biology class, there are certain criteria that make more sense than others. The "cells bounded by membranes" criterion is foolish, based only on the fact that we have only ever observed one related group of living things. It is like defining humans as light skinned after a visit to one family in Norway. The "has genetic material" criterion makes a bit more sense. I would rephrase it as "makes offspring that are more similar to themselves than would be expected randomly." The "grow and reproduce" thing is really two criteria. Growth, I think, is like the zebra's stripes. If we found beings that were built at full size by their parents, and then went on to make offspring that at the beginning of their lives were also full sized, but had high alivitude in every other way, I think we would recognize them as alive. Reproduction, on the other hand, seems a necessary component of a living system. Individuals who don't reproduce can be alive, but it is difficult to imagine a system in which life persists without reproduction. The "exchange gasses with their environment" malarkey is pure chauvinism. Most living things we know do, but is this a defining characteristic? No. "Maintains internal order by taking in low entropy mass/energy and putting out high entropy mass/entropy" is I think, inescapable for any lifeform.
So biology is (maybe) the study of entities or phenomena which make offspring that are more similar to themselves than would be expected randomly (in other words reproduce) and maintains internal order by taking in low entropy mass/energy and putting out high entropy mass/entropy. I'll have to think about this definition and see if I can think of counter-examples.