Strange questionn but never done it before and cant find info!!! I am flying from London to Rome then from Rome to Tunisa, I am flying with the same airline but am unsure of what happens or what I need to do when I land at Rome, do i have to check in again and pick up my luggage or will this be done for me???
You'll need to double check when you check in but normally with a 'traditional' airline your luggage will be transferred for you and you'll see it next in Tunisia.
Howver budget airlines (ryanair, easyjet, etc) do not do this. You have to collect your baggage and check in again.
Just to add to dzug's answer. When you check in in London you should be given a separate boarding pass for each leg of your journey. In Rome you do not need to check in again. Just watch the monitors and go the gate when your flight appears. The gates normally open 40 minutes before departure but allow yourself time to get through security.
I am flying a similar route next month, although I'll be flying from Seoul (Korea) to London Heathrow (UK) with KLM. My first trip will be to Amsterdam (Netherlands) and then after about 90 minutes, I'll change aircraft and proceed to London.
If your flights were booked at the same time, the check-in agent should automatically check you onto your onward flight. If booked at different times, you'll need to mention your connection to them and hopefully they'll make arrangements for you.