It's my fault. Forgive me for that bad term.
For a space or a subspace, not only do you have an algebraic structure (explained in the previous post like addition, constant multiplication,...), but you also have another structure which mainly measure the relationship between any two points. For example, in a Hilbert space, if x=(x1,x2,x3, ...), y=(y1,y2,y3,...), you may define the distance:
dist(x,y)=((x1-y1)^2 + (x2-y2)^2 + ...)^0.5.
In some more complicated spaces, you may not be able to define the distance between any two points like that. You may define a "norm", which essentially acts like the distance in simple cases. All those things, like distances, norms, even some more complicated forms, ... are all called topology structure.
A subspace of a hilbert space needs at least one topology structure which is usually inherited from the space itself.