SOAP stands for Simple Order Access Protocol. Its a protocol specification where messages are sent  in XML format over http protocol. For more information, please visit here.
JAX-WS is a set of API for creating SOAP web services.  It is often used with JAXB for binding i.e. to transform XML to Java objects and vice versa. Few popular implementations are CXF (By Apache), Axis2 (By Apache) and Metro (By Oracle).

Introduction

Create a simple SOAP web service document style using CXF APIs

Quick Overview of SOAP with CXF

Create a simple SOAP web service with parameter style as Wrapped using CXF

CXF SOAP Webservice Wrapped Style

Create a simple SOAP web service document style using Axis2 APIs

Quick Overview of SOAP Webservice with Axis2