some of the sounds are so quiet i cant make them out even though my speakers are banging...
"Var" means "there is", "yok" means "there isn't" (within this context). Your sentence would be like "You have don't have sugar" or literally "There is your sugar isn't there" or something : P
Well, yok means "there is not". Saying "Senin Sekerin yok" means "Your sugar doesn't exist" or "You don't have sugar" and is the opposite of var, which means "there is". To us, var may as well be interpreted as "have", and yok as "have not" in this possessive context.
According to another source, "yoktur" means "definitely non-existent", where as "vardir" means "definitely is". They are used to emphasize factual statements, which I believe was previously stated. My Turkish friends have never corrected my usage of "yok" though, so this is somewhat new to me.
Degil means "not". If you said.. "Senin Sekerein degil" that is negating the implication that the sugar was yours. So, it's like saying "(It's) not your sugar". Does this make sense?