What does what is the nature of this covenant mean in the question

Breaking down "nature of this covenant"...

Nature refers to the characteristics of the covenant

A covenant is an agreement, sort of like an informal contract

While you didn't provide us with Chapter 19, versus 5 and 6, reading the rest of the question it can be inferred God is telling the Israelites to "keep his covenant."

To answer the question "What is the nature of this covenant?" read the chapter and ask yourself the following questions:

Is God stern with the Israelites? Helpful? Angry? Happy? Does He feel bad for them? Does He take pity on them? Are they loyal to God?

Does God get more out of the covenant than the Israelites do? Who does the covenant benefit more?

How do the Israelites feel about the covenant? How do they feel about their current situation in general? Does the convenant calm them? Inspire them?

sense of self-interest