Goldman is addressing a standard problem in epistemology, namely, what it is about knowledge that distinguishes it from mere true belief. Goldman originally defended a causal theory of knowledge, which has it that a true belief is knowledge only if it has been caused in an appropriate way. In the passage you quote, he seems to be referring to a reliabilist account of knowledge, which has it that knowledge is true belief that is reliably obtained.
In order to test these theories of knowledge, he engages in a thought experiment. Jones has beliefs about his childhood based on his memories, and these beliefs are in fact true because his memories are in fact reliable. We would ordinarily say that a person has justification to believe that their childhood memories are true, because while our memories are far from perfect, some of our recollections at least are reliable and would qualify as being knowledge.
But now there comes a twist. Jones' parents lie to him about his childhood, and tell him that he suffered amnesia and a portion of his memories are false. We are not told why they do this, but Jones has reason to believe them because they are his parents, and they normally never lie to him. On a common intuitive understanding of justification (or of knowledge) we might say that his childhood beliefs are not justified, because he now has conflicting evidence for them. His memories indicate one thing, but seemingly authoritative information from a previously reliable source indicates the opposite. In cases where we are faced with conflicting evidence, often the appropriate course is to suspend belief and not suppose that we are justified in accepting either option.
But Goldman says that on the theory he proposes, Jones' beliefs would be justified, because they were acquired in a reliable way. The contrary statement from his parents does not make his senses or memories any less reliable.
Whether this is plausible is questionable. We might say that receiving information from normally reliable sources is itself part of the causal, and usually reliable, process of forming true beliefs. So, if apparently reliable information conflicts with our existing beliefs, it is quite appropriate to regard them as not justified, until the conflict is resolved.