From the recording Old Tin Can
Alex, Dan and Larissa are first-generation children of Ukrainian immigrants and grew up speaking the language and listening to the folk songs. They wanted to include this song to show everyone their mother-tongue and the foundational roll Ukrainian culture has played in their lives. (And they wanted to surprise their dad for Christmas :)
The song speaks of a Kozak who sees a maiden of surpassing beauty and tries to find out through veiled terms whether she is available for courtship. You'll have to learn Ukrainian to get more details.