I've never really been able to fully understand it.... but here goes:
Blockchain, it's the same tech used for crypto currencies (i.e. bitcoin). Basically, there's a giant sequence of numbers, everything is unique.
Not sure if this picture will help (I just took it from Wikipedia) but....
New "blocks" are added to the "chain". Each block references the prior block (in the image, they're showing that with "Prev Hash", it has a timestamp, and "new" data for it's transaction.
Because each subsequent block references the prior one, you can't change the value of a block, without affecting all future blocks. Peer-to-Peer networks are typically used to made sure new blocks are valid..... and if someone started mucking with older ones, the network would detect that.
When you hear about people "mining" bitcoins.... think of one of these blocks representing a single coin. As that chain grows, the computations needed to figure out the next block become more complex. The complexity grows with each block. People would dedicate computers to doing these calculations, and mine that coin for themselves - Which they could keep, sell, etc.
The value of bitcoin is based around the idea that there are a finite number of them, and they are verifiable as these blocks have to match their place in the overall sequence.
When I read about the use with these NBA Video things (cards?) - The company is using blockchain technology to digitally stamp the video. I scratch my head at that, and think "so what?". I understand that this means they can put a unique watermark on the video (how it was described in the article) - but I'm not sure why that makes it desirable to own...... because it will go up in value? Well, sure. There is that. If you could have bought one of these things for a few dollars, and now sell it for 100s - you're happy.
I'm just not sure why owning a video clip, that's had one of these blocks spliced into it, would be appealing.