The word "snug" means "tight", but in a positive way:
Make sure that all the straps on your backpack are nice and snug. If they're too loose, everything will move around a lot more and you'll get tired out more quickly.
But in the example at top, the speaker uses "snug" to describe her friend's pants being too tight. In other words, she's saying that her friend is fat. This isn't very positive. But people also use "snug" to describe something that's tight in a bad way, if they're trying to sound polite:
Our hotel room was nice. The bed was a bit snug, but otherwise it was all great.
The "waistline" is the area around your stomach where the top part of your pants are.