Eukaryotes are living organisms. Unlike their sister branch of the tree of life, the prokaryotes, their cells have a membrane-bound nucleus, and contain organelles called mitochondria as well as other membrane-bound organelles.
The domain eukaryote on the tree of life is an umbrella for the kingdoms of animals, plants, fungi. Eukaryotes can be multicellular, as we human beings are, or single-celled as for example amoeba are.
The four processes of life shared by eukaryotes are, in no particular order
iv) Reproduction (including Growth)
The first two processes i) and ii) are the body's (or plant's/fungi's) way of taking up required inputs from the environment. Respiration in humans for example is a process where oxygen from the air is taken in through breathing and the waste product carbon dioxide is exhaled via a gaseous exchange in the lungs. The cells of the body use the oxygen to produce energy for storage to be used for example by muscles as and when required. Digestion in humans is a process where food is broken down in the stomach and intestines, and important nutrients for cell growth and maintenance are directed towards organs or cells for further processing. Waste products such as fibre and toxins are evacuated via the colon or bladder.
The third process iii) is the body's way of pumping the inputs obtained from processes i) and ii) to the cells, either via organs first, or directly. This process is Circulation. In the human body, blood (in which cells are suspended) is pumped around the arteries and veins by the heart. The oxygen from the air and nutrients from food travel via the blood, from the lungs, or from the intestines or other organs, and can be taken in by cells. Waste products from cellular respiration are carried away by the blood and expelled by the appropriate organs.
The fourth process iv) is the process that the other three processes lead to. When the cells have enough energy from the cellular respiration, made possible by the inputs to the body, they can subdivide either by mitosis (cell replication) or by meiosis (production of gametes for sexual reproduction). The former subdivision is the process of growth as one cell becomes two (with the same DNA content as the first). Cell growth is necessary for juveniles, but also for adults where repair of tissue is needed, so that new cells produced replace dead cells. The latter subdivision produces four cells, called haploids, each with only half the DNA content (number of chromosomes) of the parent diploid/somatic cell (in humans there are 23 pairs of chromosomes, that is 46 chromosomes, so that human haploid cells have 23 chromosomes). In sexual reproduction, where male and female haploids (gametes) combine, a new diploid (somatic) cell results made up of equal amounts of paternal and maternal genetic material. For evolutionary advantage, in subdivision by meiosis shuffling of genetic material occurs so that there are genetic mutations from parent to child. Prokaryote organisms, such as Bacteria, do not reproduce sexually in this way, but asexually. Rather than gamete cells fusing together to form a new organism, the parent cell may for example undergo fission where the DNA material is unzipped into two strands. Two cells result from this fission, but they have exactly the same DNA encoding.