"Premature optimization" is a phrase used to describe a situation where a programmer lets performance considerations affect the design of a piece of code. This can result in a design that is not as clean as it could have been or code that is incorrect, because the code is complicated by the optimization and the programmer is distracted by optimizing.
When deciding whether to optimize a specific part of the program, Amdahl's Law should always be considered: the impact on the overall program depends very much on how much time is actually spent in that specific part, which is not always clear from looking at the code without a performance analysis.
A better approach is therefore to design first, code from the design and then profile/benchmark the resulting code to see which parts should be optimized. A simple and elegant design is often easier to optimize at this stage, and profiling may reveal unexpected performance problems that would not have been addressed by premature optimization.
In practice, it is often necessary to keep performance goals in mind when first designing software, but the programmer balances the goals of design and optimization.