What does this relation mean?

What does it mean to multiply an element of a group by a subgroup?

From my Discrete class notes:

Let be a group (a set with an operation that is closed and associative, has an identity and every element has an inverse). Let be a subgroup of .

, define relation as if .

Relation is called a 'coset'.

What does that relation, coset, mean? I interpret the definition as " relation if left times a subgroup equals left times the same subgroup". But that is kind of meaningless. What is an element times a subgroup?

Thanks, in advance,

Jeff