Every Time I Look, It is 01:23

In all likelihood, it means you remember seeing that particular time when you see it and don't remember seeing other times.

Probably you look at a clock often. But you only remember 01:23. The reason you remember it is because you give it a bit more attention at the moment you see 01:23 than you generally give other times when you see them.

That extra attention tends to make it stick in memory.

01:23 is a natural sequence of numbers, which may be the reason it attracted a bit more of your attention. Or, perhaps, it attracted extra attention because the minutes represent your age. There is something about it that is notable for you, something that makes you consciously and alertly notice that you are seeing the time.

If you wish to follow up the meaning of the numbers, numbers represent certain numerology energy. The energy can be interpreted. Here is a link for number 01:23.