An objective is a qualitative goal. The key results are generally quantitative numbers that can help you measure if you are achieving that goal.
An example: an objective might be "improve application performance". The key results for that objective might be "reduce average page load time from 3s to 1.5s" and "reduce API response times by 60%".
If you were to tell your CEO you're reducing page load time, they will rightfully ask you why and what problem you're solving. The objective is the simple sentence that makes the "why" clear. It might itself be subordinate to a higher level objective. The idea is that all work is clearly aligned to specific goals in a very transparent manner.
It's actually a very solid framework, but as the many comments indicate, poor implementations abound (also see Agile, DevOps, etc).
An example: an objective might be "improve application performance". The key results for that objective might be "reduce average page load time from 3s to 1.5s" and "reduce API response times by 60%".