Learning to understand the performance of a running system is unavoidable for the same reason that learning debugging is. Even if you understand perfectly precisely the cost of the code you write, your code will make calls into other software systems that you have little control over or visibility into. However, in practice performance problems are a little different and a little easier than debugging in general.
Suppose that you or your customers consider a system or a subsystem to be too slow. Before you try to make it faster, you must build a mental model of why it is slow. To do this you can use a profiling tool or a good log to figure out where the time or other resources are really being spent. There is a famous dictum that 90% of the time will be spent in 10% of the code. I would add to that the importance of input/output expense (I/O) to performance issues. Often most of the time is spent in I/O in one way or another. Finding the expensive I/O and the expensive 10% of the code is a good first step to building your mental model.
There are many dimensions to the performance of a computer system, and many resources consumed. The first resource to measure is wall-clock time, the total time that passes for the computation. Logging wall-clock time is particularly valuable because it can inform about unpredictable circumstances that arise in situations where other profiling is impractical. However, this may not always represent the whole picture. Sometimes something that takes a little longer but doesn't burn up so many processor seconds will be much better in the computing environment you actually have to deal with. Similarly, memory, network bandwidth, database or other server accesses may, in the end, be far more expensive than processor seconds.
Contention for shared resources that are synchronized can cause deadlock and starvation. Deadlock is the inability to proceed because of improper synchronization or resource demands. Starvation is the failure to schedule a component properly. If it can be at all anticipated, it is best to have a way of measuring this contention from the start of your project. Even if this contention does not occur, it is very helpful to be able to assert that with confidence.