In quantum computation, a ket is a vector in a Hilbert space. A Hilbert space is just a fancy way to describe a typical space you find in linear algebra, where the space allows you to compute lengths and angles. When discussing kets, the usual vector space is the set of complex-element vectors with unit length (or “norm”). The vectors can have any number of elements (or “dimension”), but when discussing qubits, they are 2^n-dimensional for n qubits.
(It’s important to note that a ket is not distinguishable from a vector. It’s actually called so because of a notational convention, not because it has deeper underlying meaning. However, physicists will still use the word “ket” instead of “vector” or “quantum state” even if they’re not emphasizing notation.)
More interesting, though, is how kets combine with other kets via tensor products. This ingredient is as essential to QC as flour is to cake.
This article [0] informally presents a fully general definition of a ket along with the tensor product with an emphasis on why a representation and notation was chosen. But it does require a good understanding of linear algebra already.
[0] “Someone shouts |01000>! Who’s excited?” https://arxiv.org/abs/1711.02086