-ski in Polish surnames means "from". Therefore, Galinski means "from Galiny" alternatively "from Galinki". Galiny or Galinki is a name of a village (where Galiny refers to a big village while Galinki refers to a small village - as per rules used in Polish language).
-icz or -ic refers to father. E.g. Dobkowicz means son of Dobko.
PS. I am researching Galinski familiy from Jeleniewo/Suwalki