This idiom means that you are at the end of your wit (your mental capacity). You have tried everything you can think of and you have no more ideas. Nothing has worked.

Hi Jesús, to be at one's wits' end means to be so worried, confused, or upset that you don't know what to do next. In your example sentence, the person has looked everywhere for his or her dog, and is now feeling bad and doesn't know what to do. e.g. I can't sleep because my neighbors play loud music every night until 3 am. I am at my wits' end.

Hi there, Idiom: At our wit's end When we are at our wit's end, we have exhausted every possible way to think about a problem or a solution. Example: We tried to come to an agreement on this problem, but it has become apparent that we are all at our wit's end. As for your example, you have looked everywhere for your missing dog. You can't think of any other place where your dog could be at. Probably you are feeling a sense of hopelessness now. Hope this helps. Cheers, Lance

'I'm at my wit's end' = I'm worried, confused, annoyed, upset, I don't know what to do. http://dictionary.cambridge.org/dictionary/english/be-at-your-wits-end