When I was young, Sesame Street was on the Public Broadcast Network-PBS (in US). But now I see on HBO Go/On Demand, I see that it is being shown on there now. Did HBO buy the broadcasting rights to Sesame Street and no longer being shown on PBS? What's the story behind Sesame Street and HBO?
Yes, HBO purchased the first-run broadcast rights to Sesame Street late last year.
According to The Hollywood Reporter, Sesame Workshop (the company that produces the show) was losing money for several years in a row, and needed a source of funding to maintain operations. They signed a deal with HBO that allows HBO to show the episodes first, and PBS gets them 9 months later at a small cost.
HBO is attempting to solidify a foothold in the children's programming market, to hedge off Netflix and Amazon who are attempting to do the same.
PBS has seen their profits from licensing their IP in Sesame Street drop off, with revenue only matching their production costs of 41 million in the last few years. As people, ie kids forcing their parents, stop buying DVDS or home media, in place of streaming services, PBS is not seeing the profits needed anymore.
According to the link that @KutuluMike provides:
PBS reportedly pays a license fee that covers about 10 percent of the show's annual $40 million production cost.
So for 4 million, they get twice the amount of episodes their normal 40 million budget provides, with a small delay, and they keep all the profits from merchandise and other sources. Basically HBO is paying 36 million plus for 9 months of headway, which only affects people that can afford HBO. It's pretty much transparent to people who depend on OTA broadcast PBS, or who care about seeing the episodes early.
If they didn't sign this deal, PBS would have to shut down production completely, as it is too expensive to film in the current market without a streaming service deal.