I'm not entirely sure if this is the right sub for this kind of question, as it may pertain more to an anthropologist or someone better learned in human evolution, but when exact did human beings feel the need to clothe themselves?
This is a tricky question that is particularly difficult to answer via traditional archaeological methods. The problem is pretty simple - clothing rots away. We have very little preserved ancient clothing. A notable example is the clothing found with Ötzi. Finds like this give us some insight into what ancient people wore, but the age of the find is pretty small in comparison to the age of the human species (only 5000 years compared to tens or hundreds of thousands of years, depending on your definitions).
Luckily, some clever people investigating the evolutionary history of lice are able to help us. The genomes of the lice infesting humans have been sequenced. Body lice diverged from head lice with the advent of clothing, occurring at least 83,000 years ago according to this study. Now, as food for thought, consider the ages provided by this study as a conservative estimate. People may well have been wearing clothing for a considerable time before this evolutionary divergence occurred in lice.