As a line cook on a station, your "all day" count is the total number of a given item that you have ordered in, including those that you are fired on.
All day counts become really important for items that need extra time to cook. IE those that are cooked off when or before they are ordered in. Pan roasted chickens, steaks, pork chops, duck breast all need at least 20 minutes or so to prepare. So, if in the heat of battle, you, the line cook lose track of how many chickens you need for all of the upcoming fires, you can ask your chef for an "all day" on chickens. If you don't have enough cooked off, you will need to act quickly to or risk extremely long waits for diners that are ready for their entrees.
Expediting Chef: "Order in chicken, char"
Sauté cook: "chicken char, ordered in...hey chef, can I get an all day on chickens?"
Chef: "You most certainly can." [scans the board] "You have 6 all day. Do you have enough?"
Sauté cook: "I have 4 cooked off"
Chef: "Okay, go ahead and get a pan hot and get two more cooked off"