LSP = Lootshare potential
Basically when ever you are with a team killing a boss or something, and you're using LS/CS, every time you don't get a drop, you gain LSP instead. Basically the higher your LSP, the higher your chance of recieving drops. The higher value of the items you miss, the more LSP you gain.
The LSP you gain works somewhat like Coinshare, in that it is split up between all the people who missed the drop. So for instance, if I was doing Saradomin Godwars with a 5 man team, and someone gets a Saradomin Hilt drop, the other four players gain about 15m LSP each. Since the minimum price of a Sara Hilt is 59.5m right now.
Now, if you get a drop, you loose LSP equal to that of the drop. Since the Armadyl hilt is worth 88.2m in the GE at lowest right now, I lost 88.2m LSP. Which currently puts me in the negatives, meaning I shouldn't expect any drops while in Lootshare teams any time soon.
Every day you do not do a Lootshare/Coinshare drop, your LSP get's closer to 0 by 10%. So if you have lets say 50m LSP, and you don't do some sort of trip where you're using LS/CS, you will loose 5m LSP. Now if you do a trip, you don't loose anything.
Also Note that Coinshare cash splits DO NOT affect your LSP at all, since you niether missed, nor got a drop (in a sense)
I hope I didn't confuse you