From the installation instructions:
Apache Axis is an Open Source SOAP server and client. SOAP is a mechanism for inter-application communication between systems written in arbitrary languages, across the Internet. SOAP usually exchanges messages over HTTP: the client POSTs a SOAP request, and receives either an HTTP success code and a SOAP response or an HTTP error code. Open Source means that you get the source, but that there is no formal support organisation to help you when things go wrong.
SOAP messages are XML messages. These messages exchange structured information between SOAP systems. Messages consist of one or more SOAP elements inside an envelope, Headers and the SOAP Body. SOAP has two syntaxes for describing the data in these elements, Section 5, which is a clear descendant of the XML RPC system, and XML Schema, which is the newer (and usually better) system. Axis handles the magic of converting Java objects to SOAP data when it sends it over the wire or receives results. SOAP Faults are sent by the server when something goes wrong; Axis converts these to Java exceptions.
SOAP is intended to link disparate systems. It is not a mechanism to tightly bind Java programs written by the same team together. It can bind Java programs together, but not as tightly as RMI or Corba. If you try sending many Java objects that RMI would happily serialize, you will be disappointed at how badly Axis fails. This is by design: if Axis copied RMI and serialized Java objects to byte streams, you would be stuck to a particular version of Java everywhere.
Axis implements the JAX-RPC API, one of the standard ways to program Java services. If you look at the specification and tutorials on Sun's web site, you will understand the API. If you code to the API, your programs will work with other implementations of the API, such as those by Sun and BEA. Axis also provides extension features that in many ways extends the JAX-RPC API. You can use these to write better programs, but these will only work with the Axis implementation. But since Axis is free and you get the source, that should not matter.
Axis is compiled in the JAR file axis.jar; it implements the JAX-RPC API declared in the JAR files jaxrpc.jar and saaj.jar. It needs various helper libraries, for logging, WSDL processing and introspection. All these files can be packaged into a web application, axis.war, that can be dropped into a servlet container. Axis ships with some sample SOAP services. You can add your own by adding new compiled classes to the Axis webapp and registering them.
Before you can do that, you have to install it and get it working.