First, let's describe the function of the flagella and the cilia before indicating their differences. Both, the flagella and the cilia, are basic parts of the body of cells. As many parts of cells, these two particular ones help the cell in the process of movement.
Here is how they differ: The cilia is like a protective cover made of small filaments. The molecule that makes these filaments is called kinesin, and it creates a reaction within the cells that aids with moving the cell through the human body. So, it covers the cell and helps her propel through the blood, plasma, or any fluid. This being said, the cilia is mostly found in organisms that are multicellular, because their job also helps certain body organs to work more effectively. One example is the respiratory system: The consistency and ease of movement of the cilia allows the cells to flow rapidly through the blood stream thus preventing for dust accumulations or any accumulation of particles to damage the proper function of the respiratory system. To put it in a mundane way, the cilia are the "yellow cabs" of cells.
With a similar structure, the flagella are also made of filaments and tubules that also aid in the process of transportation and movement. However, instead of kinesin, the substance that aids the flagella to help move the cell is found in the plasma membrane. The flagella is larger (longer) than the cilia, but it is also limited because it can only exist in gametes such as the sperm cell. In other words,the flagella are like a turbo added to gametes to move faster whereas the cilia is consistently moving at a steady rate.
They are different, but for each function that they perform they are equally important.