These channels are used to communicate between native code (plugins or native code inside of your project) and the Flutter framework.
MethodChannel
A MethodChannel is used for "communicating with platform plugins using asynchronous method calls". This means that you use this channel to invoke methods on the native side and can return back a value and vise versa.
You can e.g. call a method that retrieves the device name this way.
EventChannel
An EventChannel is used to stream data. This results in having a Stream on the Dart side of things and being able to feed that stream from the native side.
This is useful if you want to send data every time a particular event occurs, e.g. when the wifi connection of a device changes.
BasicMessageChannel
This is probably not something you will want to use. BasicMessageChannel is used to encode and decode messages using a specified codec.
An example of this would be working with JSON or binary data. It is just a simpler version because your data has a clear type (codec) and you will not send multiple parameters etc.