You might want to check if the TV can take the range of voltage likely to come from the boat “supply”. The battery, alternator and charger will all give voltages other than 12V. Sometimes the TV will be ok with this, but sometimes it actually needs a regulated 12V supply which is what it would get from its own 12V PSU.
The invertor will provide a stablised 240V voltage on a range of input from say 10.5V to maybe 15V. So the TV PSU will then produce exactly the right voltage for the TV.
This method does “cost” power – maybe 15% will be lost in the various conversions.