Applause! I hate the word "performance" and its evil spawn, "performant".
Do you mean speed? Efficiency? Accuracy? Say what you mean.
This is my excuse for why I have no idea what "performance optimization" entails or means. Now to convince interviewers..
In a context of an interview it means how performance of an algorithm scales with respect to the input length. This is measured in Big O notation. Understanding that is seldom very helpful on the job, but it's very important for interviews, so make sure you learn it.
That's not specific enough. Memory usage, elapsed time, and energy usage are all functions of the input size, and each is a different optimization problem. Instead of talking about performance optimization, you should be talking about memory optimization or speed optimization.
I once witnessed a very heated argument among a group of programmers discussing some code on a microcontroller. Half of them thought the performance was abysmal. The other half thought the performance was great. To everybody it was obvious to see what the performance was, why were the other half being so bone-headed about it?
Turned out the first group were trained mechanical engineers, the second were trained software engineers. For the first group, "performance" meant how closely the motion of the device attached to the microcontroller tracked the optimal path. I.e. the performance of the function approximation that the microcontroller code was doing. To the second group, it meant how fast the code ran. This was completely irrelevant to the first group, since as long as it managed to run 1000 times per second (which it easily did), nobody cared how many nanoseconds there were to spare each cycle. Why are you even talking about that? The performance is shit, we need to improve it and who cares if it takes a few more CPU cycles.