The Irish-English noun pogue, which has also been spelt poge, poage and póg, means a kiss. It is from Irish póg, of same meaning. In An Irish-English Dictionary (1864), Edward O’Reilly gave the following translations:

– pog, substantive feminine, a kiss; Welsh, poc.
– pogadh, substantive, kissing.
– pogaim, verb, I kiss.
– pogaire, pogoir, substantive masculine, a kisser.
– pogtha, pogthuighthe, participle, kissed.

Early Irish póc is cognate with Middle Breton pocq (Breton pok) and with Old Cornish poc- found in the compounds poccuil and impoc. In Lexicon Cornu-Britannicum: A Dictionary of the Ancient Celtic Language of Cornwall (1865), Robert Williams wrote:

Poccuil, a kiss. The root is poc, whence impoc, a kiss. Welsh, poc, pocan, pocyn. Breton, poc. Irish, pôg, †bôc; diminutive pogan. Gaelic, pôg. Manx, paag.

These words are from the ecclesiastical Latin (accusative) pacem, the kiss of peace, a specific use of classical Latin pax/pac-, peace.

One of the early occurrences of the Irish-English noun pogue is found in Wit and Mirth: or Pills to purge Melancholy (1719), a “Collection of the best Merry Ballads and Songs, Old and New”; “An Irish Song. Set by Mr. Leveridge” thus begins:

One Sunday after Mass, Dormet and his Lass,
To the Green Wood did pass,
All alone, all alone, all alone, all alone,
He ask’d for one Pogue, she call’d him a Rogue,
And struck him with her Brogue,
Oh hone, Oh hone, Oh hone.

The name of the Irish band The Pogues is from pogue mahone, anglicisation of Irish póg mo thóin, meaning kiss my arse *. In her novel Firefly Summer (1987), the Irish author Maeve Binchy (1939-2012) wrote:

“How’s Dara getting on minding the children by the Loire?” Fergus asked.
“It’s the poor French children I worry about,” Kate laughed. “I got a letter from her this morning and she said that she has taught them all to say pogue mahone. They think it’s Irish for good morning.”
Fergus laughed. “Knowing the French I’d say they’d be pleased to think their children were being taught anything as racy as kiss my arse. A very lavatorial sense of humour, I always found.”

* cf. meaning and early occurrences of ‘kiss my arse’