Certain items, such as Banshee's Veil and Guardian Angel have cooldowns related to their effects. The effect goes off and then it can't happen again for X amount of time. You can tell when the cooldown ends, because you get the blue bubble for Banshee's Veil and you get a buff for Guardian Angel.
These indicators are all well and good, but sometimes you are left thinking "Now how long ago did my Veil get hit?" Because if the Veil was about to come off cooldown, I might wait 10 seconds before going for that gank. If I would have to wait for a minute before it came off cooldown, I might go right away.
If it were to display item cooldowns the same way it indicates the cooldown for abilities and summoner spells, it would be of great benefit at times.
Some champions' passives, such as Anivia, are in the same boat as items in that it can be hard to tell exactly when it will come off of cooldown. If these could be looked at at the same time, that would be even better.
I'm assuming this wasn't originally done because the tech wasn't there. Hopefully it exists now so that we can have a little more knowledge about our champion's abilities and items.