"곰이 학교까지 걸어가요."
Translation:The bear walks up to the school.
If this was the whole sentence, then you're right, there's no difference. If, however, this is a fragment of a more complicated sentence then a difference between "up to" and "to" could be more discernible. Plus you want to cement in your mind the importance of the 까지 suffix so you that you can use it correctly when you start making longer, more complex sentences.
There are 3 forms of this word that I know of:
걷다 which is "to walk"
걸어가다 which is "to go by walking"
걸어오다 which is "to come by walking"
Here, the Korean and the English translation are specifying that, rather than the bear simply walking in the direction of the school, the bear's destination is the school itself, and is walking to go there.
So, a more apt situation to just use the simple 걷다 would be:
곰이 길에 걸어요
The bear walks in the street.
Hope that helps :)