In our somewhat warped way of thinking, we tend to get a feel of other people - especially people we don't know - based on their outward appearances. On the one hand, this might seem subjective, but our brains have to have a way of filtering the information we receive in order to protect us. So we put new people we meet into various categories and file them in the cavernous storage systems of our mind. As a result we have a host of idioms that point to that, such as: "Clothes make the man", and "You only have one chance to make a good first impression".
Fifteen years ago (when I was obviously younger), as a very hands-on event producer/director, I would be in the trenches with the crew and various vendors, dressed in old jeans, sneakers and t-shirt. I asked an employee of one of the vendors I had contracted if I could borrow his ladder for a moment and I got a rude retort from him. Some time later, I saw the manager of the vending company and recounted the story to her and she was terribly embarrassed and furious, "Does he know who you are?" she fumed. Apparently not, but that isn't the point. The point is that I did not fit into his category of what a director should look like. I was dressed like the rest of them, was too young, wasn't shouting orders, didn't elicit any fear from the crew and didn't approach him with a sense of entitlement. I thought it quite funny when I later got a rather sheepish apology from him because I understood what had happened.
But watching what you wear is not just about making an impression for other peoples' benefit. What you wear has an effect on how you feel about yourself and even how you move. The way I carry myself in a suit is quite different from the way I carry myself in shorts and flip-flops. On days I'm not feeling too hot, dressing extra dapper than usual with a splash of color usually does the trick. It really is a two-pronged effect: I feel better about myself and people respond more warmly to me, which makes me feel even better!
So Mum was right: press your shirts, polish your shoes, tuck your shirt in, brush you hair...and the world is a better and more beautiful place.