What does it mean that pragmatics is about accounting for the ability of speakers and addressees to invoke a common ground in relation to which a very wide range of language uses can be interpreted?

The statement in question means that:

Since the pragmatics is responsible for the context of a conversation and not for the meaning of the sentence used, it is likely that if the speaker and the recipient are not in the same context, or as the text mentions, they have not invoked a common ground, there will be different misunderstandings of the "grammatical form", because the "consecutive act" (context) is not the same.

Explanation:

Pragmatics serves to identify that the context has a lot to do with the meaning of a sentence and, if the two people who act in the conversation (the speaker and the recipient) are not within the same context, there will surely be many misunderstandings, this you can identify it when your parents at home or your teacher at school have asked you to do some activity and you have done something very different from what you requested despite trying to do well, this is because your context (or approach could be said ) is very different from that of your parents or your teacher at the time of assigning you the task in question, that change between what your parents or your teacher (speaker) wanted to mention and what you did (recipient) is what the branch usually studies of linguistics known as pragmatics.