Disgusting, rude, greedy, or thoroughly nasty — the way you would describe a person's behaviour if you wanted to compare them to a pig. "A swine" is an old word for a pig, and in English, calling someone a pig has long meant they are greedy, dirty, or cruel. "Swinish" is the adjective for that.

So "swinish manners" means eating and behaving in a way that turns people's stomachs. "A swinish thing to do" means a mean, low, selfish act. It can also stretch to mean simply awful or miserable — "swinish weather", "a swinish week" — where no pig is really in mind any more, just the feeling of something horrible.

This is a literary, old-fashioned word. You will meet it in novels and in angry writing; almost nobody says it in everyday conversation now. When it is used today it sounds either very British or deliberately dramatic. It is a strong insult, not a gentle one — softer than a swear word, but harder than "rude".