There were actually two 3rd Class passengers with the same name of Katherine Connolly, only one of whom survived. The Katherine who died (and was better known as Katie) was from Tipperary. She left behind a widowed mother (also called Katherine), an older sister Margaret, who suffered from tuberculosis and earned a little money from giving music lessons, and two younger brothers - Edward (a knife sharpener) and Richard (a porter). All of the Connollys had reached middle age, but none, it seemed, were earning adequate wages.
It's not entirely clear whether Katie was going to America for the first time, or returning after a visit home to Ireland, but in either case her intention was at least partly to earn money to help support her family, who received payments after her death from both the American Red Cross and the British Relief Committee.