Last call means exactly what it sounds like — the last opportunity for you to order a drink, period. If you’re at a bar and the bartenders shout out last call, that means you have a reasonable amount of time, usually 10 to 15 minutes, to head to the bar and order one last drink before closing. And yes, I said ONE drink.
Last call means the bar is getting ready to close, either because they are mandated by law to close at a certain time, or because the staff has worked a full shift and it’s time to go home. I realize you are probably having a great time, but that doesn’t mean you should act like an ass and order two or more drinks to nurse. You also shouldn’t approach the bar well after last call was announced and expect to still be served, then throw a tantrum when you are turned down.
The polite way to behave when last call is announced is to order one more drink if you are in the mood, consume that drink in a timely manner, tip well, and then head out so that the staff can clean the bar and head home for the night. Behave this way, and you can count on the staff to remember you in the future.