I just heard a person stating his opinion saying something like "If that's what they want, that's their end, but I personally don't agree."

In a sporting context, you could say that one team or individual was at one end (of a field or playing area). Eg, players change ends in both tennis and cricket. Without more context it is hard to be sure however.

We would need a little more context to be able to tell you what it means. Could you include the paragraph that it is in?