Vectors are points in some finite-dimensional space. For example, a set of geographical coordinates (latitude, longitude) is a two-dimensional vector. A list of 7 timestamps retrieved daily during a week corresponds to a seven-dimensional vector.
In linear algebra, vectors are objects that can be added together and that can also multiplied by numbers (scalars, in linear algebra language) to compose new vectors.
Here is a graphical example: adding the vectors [1, 2] and [2, 1] results in vector [1 + 2, 2 + 1] (or [3, 3]), as shown below.
Reference: Grus, Joel. “Data Science from Scratch”. O’Reilly. 2015