What it means
An Irish intensifier meaning very, extremely, or seriously. Fierce cold, fierce busy, fierce good. It replaces very in almost any sentence and adds a dramatic Irish flavour to whatever follows. Not aggressive despite the word itself. When an Irish person says it was fierce mild today, they are just saying the weather was surprisingly warm, not picking a fight with the thermometer.
Usage examples
"The queue at the post office was fierce long today, I aged three years standing there. The woman in front brought a camping chair and was the smartest of us."
"It was fierce cold this morning, I could barely feel my hands."
"She's fierce busy this week, won't have a minute till the weekend."
"That chipper was fierce busy after the match, there wasn't a hope of getting served quick."
"Your one was fierce nice about it, to be fair, not a bit awkward."
Where it comes from
This is just the ordinary English word fierce doing a very Irish little shape-shift. In Hiberno-English it lost a lot of its literal angry bite and settled into life as an intensifier, meaning very or seriously. That usage has been around in Irish speech for ages and is heard right across Ireland.