A sex chromosome is the set, usually a pair, of chromosomes that have at least one (and certainly not all) of the genes that turn on one sex-determining pathway or another. I animals, this is whether eggs or sperm (or both!) will be produced. In plants, it is whether pollen or ovules (or both!) will be produced.
To talk more about humans, the non-sex chromosomes, the autosomes, are typically found in two copies in every person, while the sex chromosomes are different between the sexes. Typically genetic females have two X chromosomes while genetic males have an X and a Y chromosomes. But, in humans, there are many cases where the sex chromosomes do not match those typical expectations.