There are three approaches to the question of belts during davening. Either a belt is necessary when the heart is not properly separated from one’s private parts (say, if someone were wearing a robe without underwear), or it is necessary if one generally wears a belt throughout the day, or it is necessary even if one does not usually wear a belt during the day. According to the first opinion, wearing a belt really has to do with the general requirement of ensuring that the heart does not “see” one private parts during prayer. According to the latter two approaches, it would appear that the idea is related more specifically to preparing in a special manner for tefillah (Shabbat 10a).
A common custom is to wear a gartel either in accordance with the last approach or because it signifies the differentiation between what is higher and lower about people. From this perspective, physical drives and needs are lesser, grosser, more debased. They could weigh down the mind, heart, and soul so we tie them off during prayer.
Our physical drives do, so often, hold us back. They can lead to sin, yes, but they can also lead to broader and technically permitted impairments like sleeping too little, eating food that is bad for us, pursuing things that don’t matter at the cost of the things that are really important. And so, while most of us do not wear a gartel, the point is well taken. When you see one, consider the point it makes since not one of us is above the folly of errors, sins, and misplaced efforts.
