SOAP - "Simple Object Access Protocol"
SOAP is a method of transferring messages, or small amounts of information, over the Internet. SOAP messages are formatted in XML and are typically sent using HTTP (hypertext transfer protocol).
Rest - Representational state transfer
Rest is a simple way of sending and receiving data between client and server and it doesn't have very many standards defined. You can send and receive data as JSON, XML or even plain text. It's light weighted compared to SOAP.