Just to clarify, there are two common ways for a relay to fail and the datasheet mentions both.
The relay can have a mechanical problem, like the spring wears out. That has a 10^7 switches min. lifetime on this datasheet.
Or the relay contacts can wear out, typically due the the small arcing that happens when you switch higher currents, so that depends on the current and voltage switched. At 10A 125V AC, it is spec’ed to last 10^5 cycles but at 10A 250V AC, that drops to 5 x 10^4 cycles. They also specify a resistive load, since there can be more arcing with capacitive and reactive loads.
You should always choose a relay that has a considerable safety margin for the load you are switching. Motors are particularly bad to switch and need more careful relay selection. Bigger motors are really good at welding the relay contacts together which is scary when you can’t turn it off–don’t ask me how I know this!
In a really high-current situation, you can use a small relay like on the relay shield, to energize the coil on a much larger relay to switch the load.
So to bring it back to your question: your TV won’t be a problem, but your AC might. Lights up to a few hundred watts total shouldn’t be a problem but really large wattage switching requires more design.