What does stream mean? What are its characteristics?
Many data-structures (lists, collections, etc) act as containers - they hold a set of objects. But not a stream; if a list is a bucket, then a stream is a hose. You can pull data from a stream, or push data into a stream - but normally only once and only in one direction (there are exceptions of course). For example, TCP data over a network is a stream; you can send (or receive) chunks of data, but only in connection with the other computer, and usually only once - you can't rewind the Internet.
Streams can also manipulate data passing through them; compression streams, encryption streams, etc. But again - the underlying metaphor here is a hose of data. A file is also generally accessed (at some level) as a stream; you can access blocks of sequential data. Of course, most file systems also provide random access, so streams do offer things like Seek, Position, Length etc - but not all implementations support such. It has no meaning to seek some streams, or get the length of an open socket.
From I/O Streams (though in java, the meaning is the same in C++ / C#)
An I/O Stream represents an input source or an output destination. A stream can represent many different kinds of sources and destinations, including disk files, devices, other programs, and memory arrays.
Streams support many different kinds of data, including simple bytes, primitive data types, localized characters, and objects. Some streams simply pass on data; others manipulate and transform the data in useful ways.
No matter how they work internally, all streams present the same simple model to programs that use them: A stream is a sequence of data. A program uses an input stream to read data from a source, one item at a time.
In C#, the streams you have mentioned derive from the abstract base class Stream. Each implementation of this base class has a specific purpose.
For example, FileStream supports read / write operations on a file, while the MemoryStream works on an in-memory stream object. Unlike the FileStream and MemoryStream classes, BufferedStream class allows the user to buffer the I/O.
In addition to the above classes, there are several other classes that implement the Stream class. For a complete list, refer the MSDN documentation on Stream class.
There's a couple different meanings. #1 is what you probably mean, but you might want to look at #2 too.
In the libraries like those you mentioned, a "stream" is just an abstraction for "binary data", that may or may not be random-access (as opposed to data that is continuously generated, such as if you were writing a stream that generated random data), or that may be stored anywhere (in RAM, on the hard disk, over a network, in the user's brain, etc.). They're useful because they let you avoid the details, and write generic code that doesn't care about the particular source of the stream.
As a more general computer science concept, a "stream" is sometimes thought of (loosely) as "finite or infinite amount of data". The concept is a bit difficult to explain without an example, but in functional programming (like in Scheme), you can turn a an object with state into a stateless object, by treating the object's history as a "stream" of changes. (The idea is that an object's state may change over time, but if you treat the object's entire life as a "stream" of changes, the stream as a whole never changes, and you can do functional programming with it.)