What Happens When You Try To Watch Something In 1080p Resolution On A 720p Resolution Screen?

Assuming the TV can even accept 1080p input, it will scale it down to its native resolution: 720p
Quality depends on the source and scaler quality difference between TV and source.
Example 1. Source is a 480 movie, upscaled to 1080p. TV will downscale back to 720. two scalings = no good. Better let the source output at 720p.
Ex. 2. Source is a 1080p movie. TV will downscale to 720p. Alternative is to let the player downscale to 720p.

Most 720 TV’s can accept up to 1080i signals, but not progressive.
Read owners manual to confirm.
When you do input a 1080i signal it will show, but the signal will be down converted (internally) to what ever the native resolution of the panel is, which in this case is 720.
Will you see any difference? Probably not.

no it wont be any better of a picture because 720p is the maximum resolution of the screen.

340p are missing.
nothing. just won’t be as perfect of a picture.