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A flag variable is a boolean variable (usually with the values 0 and 1 or false and true, respectively) that acts as a signal to control the flow of a program based on whether certain conditions have been met or a specific process has been completed. It is often initialized with the value 'false' (0) and set to the value 'true' (1) when the condition is satisfied.

Let's consider an example to better understand the use of a flag variable. Suppose we have a list of integers, and we want to check if the list contains a specific number, say, 42. We can use a flag variable to achieve this. Here's how: 1. Initialize the flag variable (found) with a 'false' value. 2. Loop through the list of integers. 3. For each integer, check if it is equal to the target number (42). 4. If the target number is found, set the flag variable (found) to 'true' and exit the loop. 5. After the loop, check the value of the flag variable (found) to determine if the target number was found in the list or not. The flag variable helps in controlling the flow of the program depending on whether the target number was found or not.