Knowing low level stuff can help a lot.
To become a racing driver, you have to learn and understand the basic physics of how tyres grip the road. Anyone can learn to drive pretty fast, but you need a good understanding of the "low level" stuff (forces and friction, racing lines, fine throttle and brake control, etc) to get those last few percent of performance that will allow you to win the race.
For example, if you understand how the CPU architecture works in your computer, you can write code that works better with it (e.g. if you know you have a certain CPU cache size or a certain number of bytes in each CPU cache line, you can arrange your data structures and the way that you access them to make the best use of the cache - for example, processing many elements of an array in order is often faster than processing random elements, due to the CPU cache). If you have a multi-core computer, then understanding how low level techniques like threading work can gave huge benefits (just as not understanding the low level can lead to disaster in threading).
If you understand how Disk I/O and caching works, you can modify file operations to work well with it (e.g. if you read from one file and write to another, working on large batches of data in RAM can help reduce I/O contention between the reading and writing phases of your code, and vastly improve throughput)
If you understand how virtual functions work, you can design high-level code that uses virtual functions well. If used incorrectly they can severely hamper performance.
If you understand how drawing is handled, you can use clever tricks to improve drawing speed. e.g. You can draw a chessboard by alternately drawing 64 white and black squares. But it is often faster to draw 32 white sqares and then 32 black ones (because you only have to change the drawing colour twice instead of 64 times). But you can actually draw the whole board black, then XOR 4 stripes across the board and 4 stripes down the board in white, and this can be much faster still (2 colour changes, and only 9 rectangles to draw instead of 64). This chessboard trick teaches you a very important programming skill: Lateral thinking. By designing your algorithm well, you can often make a big difference to how well your program operates.