A keyword is your unique identifier. This is what you will use to receive inbox messages.
A contact will send an SMS "KEYWORD this is a sample message" to 20642 and this message will make its way to your Inbox so keep it simple.
SMS templates are commonly used messages that you can pre-compose for use.
Add them here : Create SMS Templates..
Contact groups as the name suggests are simply groupings of contacts.
This contact groups can be based on anything you choose and will help you target a bulk message. A sample contact group can be Male Customers, you can then create/import male contacts tagged to this group for targeting.