Staying warm has been mentioned already, though, consider both rain, and wind. Wind can drop the temperature you are experiencing quite quickly. And, of course, in very hot places, some clothing can help keep you cool by keeping the direct sun off your body.
Places warm enough to go without clothing usually are also warm enough to be teeming with insects. Clothes are not a perfect protection, but people quickly find if they have to deal with bug bites there are places far less comfortable to get them - and those spots get covered up.
Then, of course, there's daily life - walking, grabbing and carrying stuff - it's easy to get chaffed, scraped, or blisters, and certain types of clothing can help against that. Many people develop some form of sandals or shoes pretty early in making clothing, just for the sake of protecting the feet and toes.
Pockets! Pockets are useful. People quickly find the small pouches and bundles that you can make relatively easily become logistically unwieldy, especially if you need to keep many objects available and organized.
Even in the most bare bones society, the first person who usually needs this is your healer/medicine person, since they'll have to deal with a lot of plants and materials.
Decoration matters. Being able to hide a bit of belly fat, or wrinkles on your legs is a baseline thing a lot of people find useful for their appearance. Some colors work better with some folks than others.
In a completely different direction, you might want to intimidate or scare someone, such as enemies from a rival group. Monstrous masks, broadened shoulders, shoes that sound loud and heavy...
Who is the leader? Who is the holy person? Usually in nearly every society, those two folks get special clothing first. That's because there are expectations with how you act and treat those people, different than others. Allowing people to see this, easily, allows people to know how to act. This also directly ties to "passing down the cape" as a generational act of roles.
The more respect or changes in behavior that are expected between roles, the more you'll see specific markers to be worn to display that. One of the earliest and most common ones is "adulthood". In hunter societies, unsurprisingly, if you hunt a fearsome predator, wearing the skin is an indication of your skill.
Once you can successfully decorate your clothing with some kind of dye or paint, or weave colors of different materials together, you can create decorations and portable historical records. It's not surprising that many cultures have history in blankets, cloaks, tents, skirts, and so on.