Great - finally got there... What Az said is basically it.
You cannot "watch" a game live. However you can save a game as a replay. Other people can send you theirs. As long as the replay is for the same version of the game you have, you can watch it. What the replay file does is re-create the game except it is in read-only mode - think of it like a movie script and the game engine is the movie projector.
Latency is also known as your PING time - it is the amount of time it takes for a packet (technical term for a collection of data bundled together to be sent over a network/internet) to be sent to the recepient and then for the other end to acknowledge it.
It is important for Sins as it uses TCP (which gurantees delivery unlike UDP). Known as a 3 way handshake, it works like this
You > Here is some data
Other person > Thank You
You > I acknowledge your thank you
If You don't get a thank you, you resend the data.
If Other person doesn't get an acknowledge your thank you, they resend the Thank you
Probably confuses you - if so go with Az's answer - time to send data end to end.