Object level vs. Meta level is a distinction between levels of abstraction. The object level usually is about a specific issue at hand, while the meta level is about general principles, 'arguments about arguments', or 'thinking about thinking'.
Example 1: "You should care about climate change because of the greenhouse effect" is an object-level argument, while "you should care about climate change because the majority of scientists agree it is a problem" is a meta-level argument.
Example 2: Planning a project is an object-level thing to do, while doing a project management course is a more meta-level thing to do.
It is often useful to move up and down the ladder of abstraction to get points across clearly. Concrete object-level examples are easy to grasp and can provide grounding, while describing a concept on the meta-level is helpful for applying it to a broad domain.