For questions about vector spaces and their properties. More general questions about linear algebra belong under the [linear-algebra] tag. A vector space is a space which consists of elements called "vectors", which can be added and multiplied by scalars. In other words, these are the spaces where we can make sense of linear combinations.
This tag is for questions concerning vector spaces, including those which concern mappings between them, both in general and specific examples thereof. More general questions about linear algebra belong under the linear-algebra tag.
A vector space consists of a set of elements called "vectors" and is associated with a field (a set with well-behaved notions of addition, multiplication, subtraction and division) called the "field of scalars". An individual vectors can be multiplied by elements of the field of scalars to produce a new vector in the vector space, and pairs of vectors can be added or subtracted to produce a new vector as well. A full introduction can be found on Wikipedia.