If L=(a
1)(s
1) + (a
2)(s
2) + ... + (a
n)(s
n) where a
1, a
2, ... ,a
n are
scalar and s
1, s
2, ... s
n are
vectors, then L is a
linear combination of s
1, s
2, ... , s
n.
In English, that means that if you have some vectors, which are just n-tuples (pairs of numbers, or triplets, etc.), and you take a combination of them, for example one of the first, three of the second, and none of third, then that combination is called a linear combination of those three vectors. The reason it's called "linear" is because you are just taking a multiple of them, you're not multiplying them by anyting nasty, or squaring them, or anyting like that.
This term is used a lot in linear algebra.