Local guardian is the guardian in charge apart from the student parents when the student is studying at a distant place from his/her family. In this case the Local guardian becomes the signing authority in place of the parents.

Now if you stay with your parents then you have no need to provide local guardian name. If its a compulsory field i.e., without filling it you can submit your application then you can put your fathers/mothers name in it. But in general the local guardian profile is usually optional.

I hope this answer helps. All the very best for your future endeavors!