When a new contract is created in CRM, it is in the Draft state and cannot be utilized to assign a case against it.
For a contract to be available, it must be activated. A contract is automatically activated by CRM if the following conditions have been met.
1. There must be contract lines added to the contract. 
2. The contract should be invoiced. You can invoice a contract from the actions menu as is shown below
3. Once the above two conditions have been taken care of, the contract status would automatically activate once, the system date matches the contract start date 
Hope this solves the mystery about activating a contract. Just like a contract is activated, the contract is de-activated automatically by CRM once the contract end date passes.