What is clock cycle in a microprocessor?
In simple terms, you can think of the clock rate as the minimum time to execute a simple operation like 1+1 or i=0.  So something like 1+10+2-100 might take around 4 clock cycles to complete.  So a 1 Mhz clock rate will get you around 1,000,000 of these simple instructions per second and if your program's logic is simple then you will probably not need to use all of those calculations each second.  On the other hand, the 200 Mhz clock rate will get you almost 200,000,000 instructions per-second.  I'll let you think about how this works for the other examples but for the laser timer this will mean that you can count to much higher numbers in the 200 Mhz microcontroller under the same conditions which means you'll have a much better resolution of time.  This can mean reacting to things faster or doing more math in the same amount of time.

The reality is more complex than this and modern compilers are excellent at making things more efficient so it can be hard to actually estimate by looking at your code how long something will take to run but this concept is generally good enough.