To understand what a layer file is, you need to understand what a layer is (this discussion is very relevant for that: What's the difference between feature class and feature layer?).
A layer (.lyr) file is simply a persistent (file-based) representation of a layer.
Neither contain any actual geographic data, only a reference to the data along with some properties about how to render it (properties for symbology, labeling, etc.).
One thing to be aware of is that if your layer references a database connection that that connection information is stored in the layer file. This can be a very bad thing from a security standpoint. Passing user login credentials around in layer files should be avoided. To avoid storing user names and passwords in layer files, the "Save username and password" box should be unchecked before using an SDE database connection file. See "Connecting to a database" for more information.