The two characters combine phonetically to sound like “Hamburg.” It's a perfect example of how Chinese adopts foreign words. The literal meaning “Han fortress” has no connection to the food itself, which is a common and important feature of many Chinese loanwords.
The 汉堡 is not just a food in China; it's a cultural symbol of globalization and Western influence. While China has its own traditional “sandwiches” like the delicious `肉夹馍 (ròujiāmó)`, the 汉堡 represents a different kind of lifestyle that became popular starting in the late 1980s and 1990s. The arrival of McDonald's (麦当劳 - Màidāngláo) and KFC (肯德基 - Kěndéjī) was a major event in major Chinese cities. For a generation, eating a 汉堡 was seen as modern, cosmopolitan, and even a bit of a luxury. It symbolized a connection to the outside world.
Today, the novelty has worn off, and the 汉堡 is simply a normal, convenient food option, especially popular among young people and families with children.
“汉堡 (hànbǎo)” is used exactly as “hamburger” is in English. You use it when ordering food, making lunch plans, or discussing food preferences. It's an informal, everyday word. You'll see it on every menu at Western fast-food chains. Interestingly, many chains in China have localized their offerings. You might find a “Sichuan Spicy Chicken Burger” (香辣鸡腿堡) at KFC or other unique flavors designed to appeal to local palates. These are still all called 汉堡. The term almost always refers to the food. While it also means the city of Hamburg, Germany, this usage is far less common in daily conversation and would be clear from context (e.g., talking about travel or German geography).