What Pheonyx means is probably
List<List<string>> listOfList;
However, note that this list contains reference types again, so you have to instantiate every element on its own. For instance:
var listOfList = new List<List<string>>();
listOfList.Add(new List<string>());
listOfList[0].Add("Some string");
listOfList.Add(new List<string>());
listOfList[1].Add("Another string");
listOfList[1].Add("Final string!");