Liandri's gives decent ap (since ap items lost some raw ap values).
It gives decent flat magic pen - valuable vs squishy enemy teams who do not build early magic resist. Think about how "lethality" (a scaling version of flat ARMOR PEN) was so strong on physical damage champs awhile back - liandri's and sorc boots are basically the ap equivalent of lethality items.
It gives some minor %hp damage which is an added bonus.
It works great on champs that can SPAM spells (ex: orianna, syndra, etc.) or have long lasting spells like rumble q and ult because they can maximize the application of the %hp damage.
The minor amount of hp it gives is enough to escape some early game trades where other items would not allow you to survive. Abyssal vs ap champs or zhonya vs ad champs would give similar levels of survivability, but sacrifice some damage potential at the 1-2 item mark.