The Port refers to Port Glasgow, a town in the west coast of Scotland. People who aren't local tend to confuse Port Glasgow with the city called Glasgow, so the Port works as a nickname to avoid this confusion.
Port Glasgow is next to Greenock and smaller places like Kilmacolm and Langbank. It's home to the Port bird.
"Where are you from?
"Port Glasgow."
"Oh I love Glasgow!"
"I'm not from Glasgow, I'm from the Port!"
The Gibby is an area in the east end of Greenock, Scotland that is home to social housing developments. There are also some privately owned properties but most residents can't afford their own home. There's a community cafe and a kids' nursery school, plus Bogston train station.
Och, here mate, you going up the Gibby?
In the Inverclyde area of Scotland, slice refers to square sausage (sometimes called Lorne sausage). Some other areas of Scotland may use the term "slice sausage", but using slice to mean square sausage only tends to be used in Inverclyde.
"This breakfast pack has hash browns, black pudding, sausages and slice."