In the world of the Culture, hyperspace (and ultraspace) are merely states existing above (and below) the mundane 3D world of existence. Physical objects in realspace don't have any physical presence in hyperspace, so it's possible for an object moving in realspace to briefly enter hyperspace, pass through the object and the emerge back into realspace on the other side, as if it hadn't encountered the object at all.
The ship decided to attempt to contact the artifact in a more direct manner; it would send a drone-probe underneath the object in hyperspace, below the surface of space-time; effectively making a tear, a rent in the fabric of the skein - the sort of opening it would normally create to fashion a way into HS through which it could travel. The drone-probe would attempt, as it were, to surface inside the artifact; if there was nothing there but a projection, it would find out; if there was something there, it would presumably either be prevented from entering it, or accepted within. The ship readied its emissary.
Warping is the name of the travel process that allows tunnelling through hyperspace (or ultraspace) in order to get to a specific location as well as allowing travel at FTL speeds in realspace.
It had been successively fitted with ever-more efficient and powerful drives and engines, until eventually it was able to maintain a perfectly respectable velocity either warping along the fabric of space-time or creating its own induced-singularity pathway through hyperspace beneath or above it.
In other words, merely entering the realm of hyperspace (or ultraspace) has no effect on your position in relation to other objects. Unless you warp somewhere, you're just sitting there.
What's remarkable is that this Mind used a combination of warp (movement in space) and hyperspace (movement in dimension) to end up inside a physical object, one with a large enough gravity well to drag an object out of hyperspace, and to somehow do so without catastrophically destroying itself and the object.
