1080i is a term related to high-definition televisions. The 'i' in 1080i stands for 'interlaced', meaning the TV draws lines and interlaces them to show the whole picture. The '1080' in 1080i means there are 1080 lines of resolution.

I have a laptop with a screen resolution of 1366x768 and i was told it was a 1080i resolution

I'm not entirely sure

you can't do that. 1080i games can be played with a hdmi cable or else it will be at 720p

Most modern LCD/Plasma TV's are capable of receiving and displaying 720i, 720p, 1080i and 1080p signals. Therefore your TV, if it can receive 1080i, should be quite happy with a 1080p signal.

No, only 1080i. 1080p is currently only found on local video sources such as games consoles and computer displays. Broadcasters are currently using only 1080i and 720p as their HD formats.