It means you can stream to arbitrary destinations rather than just to memory.

If you want to write something to a file, why would you want to create a complete copy in memory first? In some cases that could cause you to use a lot of extra memory, possibly causing a failure.

If you want to create a byte array, just use a MemoryStream:

var memoryStream = new MemoryStream();
serializer.Write(foo, memoryStream); // Or whatever you're using
var bytes = memoryStream.ToArray();

So with an abstraction of "you use streams" you can easily work with memory - but if the abstraction is "you use a byte array" you are forced to work with memory even if you don't want to.

You can easily make a stream over a byte array...but a byte array is inherently size-constrained, where a stream is open-ended...big as you need. Some serialization can be pretty enormous.

Edit: Also, if I need to implement some kind of serialization, I want to do it for the most basic abstraction, and avoid having to do it over multiple abstractions. Stream would be my choice, as there are stream implementations over lots of things: memory, disk, network and so forth. As an implementer, I get those for "free".

if you use a byte array/ buffer you are working temporarily in memory and you are limited in size

While a stream is something that lets you store things on disk, send across to other computers such as the internet, serial port, etc. streams often use buffers to optimize transmission speed.

So streaming will be useful if you are dealing with a large file