CFD stands for contract for difference.
A CFD account allows you to take the profit or loss between a buy and sell position (or vice versa if you are short) across a number of different instruments, including shares, forex, commodities and bonds. This means you do not actually purchase the shares, and thus do not pay capital gains tax or stamp duty.
All the shares listed under the live accounts are also listed under the demo accounts. That means if the share is not listed under the demo, it also will not be listed under the live account.
However, the share you mentioned, NAOV, seems to be listed under the CFD account on my live and demo CFD account, so I am not quite sure what the problem is. I have attached a screenshot below of the ticker.