This is the 3981st most frequent Russian word.
иркутского
"Iркутского" means "of Irkutsk" (relating to the city or region of Irkutsk in Russia).
'Иркутского' here is used as an adjective derived from 'Иркутск,' denoting relation to Irkutsk, a city in Siberia.
Я недавно посетил музей иркутского искусства.
I recently visited the museum of Irkutsk art.
In this case, 'иркутского' describes the 'region,' specifying that it pertains to Irkutsk.
Этот студент изучает историю иркутского региона.
This student studies the history of the Irkutsk region.
Here, 'иркутского' modifies 'мастера,' indicating that the master is associated with Irkutsk, either by origin or profession.