I classified this image in ArcGIS 10.3, but my Professor said the pixels are big and I should make it smaller. This is my problem: is there any tool that can use to make the picture grains finer. Or are there any parameters i can adjust in order to make the grain size smaller.
You should check your Environment Settings and adjust the Cell Size to an appropriate cell size: ArcGIS Cell Size
I would hazard to guess that your Professor is asking that your classification be done at a finer resolution than you've presented here. If the image you show is at the same cell size as the original image then changing the resolution does not change the fundamentals of the classification. If you reduced the resolution from the original image to process faster or to present the final product in a more generalized way, then you should go back to the product before you generalized (or re-sampled) the image.