Define "Working a tile"

I need to better understand the term "working a tile". Does it mean just having an improvement built on it.....having a Worker assigned to it constantly......going to the citizen management and assigning a citizen to that tile.....or what?

If I have a tile in my City, such as food, when do I reap the benefits? Is it every turn....only if I 'work the tile'....assign a citizen...or what?

Finally, if I have a food icon in a tile, is it for the city or the civ? The city is 'starving', so I'm looking to solve this (not much gold and the 'purchase' screen doesn't offer any food bearing buildings).

Thanks so much!!!!!!