I don't have medical training myself, so my own understanding is only that of an interested layman who's been following this closely. So please take what I say with a grain of salt, but here's my understanding of what Dr Baric said:
In the first paragraph he speaks of evidence that immunity waned over time in the case of a closely related disease called MERS.
In the second paragraph he talks about the mystery of how all human coronaviruses (including some of the viruses that cause the "common cold", the virus that causes MERS, and SARS-Cov-2: the virus that causes COVID-19, aka "The Coronavirus") keep themselves alive in the human population. He didn't say so explicitly, but the implication is that we should expect these coronaviruses to die out as humans get sick, recover, and acquire immunity to them.. but that's not what happens. People get sick with these same viruses again and again and again.
In the case of the flu (which is not a coronavirus), the way it keeps reinfecting people is that it mutates a lot in ways that will evade acquired immunity, so any immunity a person had from having had and recovered from the flu will not keep them from getting sick with another, mutated variation of the flu.
But that doesn't happen with human coronaviruses. People keep getting infected with the same strain. So the educated guess (the hypothesis) is that being infected and recovering from the coronavirus does grant some immunity, but that immunity quickly fades and then people get reinfected with the same strain because they no longer have that immunity (or have too little of it to keep from getting infected).
Then he mentions reports from China of people getting infected with the coronavirus, recovering, and then getting reinfected (which should support the above hypothesis, but we can't be sure because China has not been actually monitoring the levels of antibodies in infected and recovered people in their population).
In the final paragraph, Baric says he expects the US health care system to closely track the level of antibodies in infected and recovered people over time, which should give us some insight in to whether this hypothetical reduction in immune response really does happen.