While viewing the list of images or files within the DropBox app, place your finger on the file you want to delete and swipe to the right. Afterwards, tap on the Trashcan icon to delete it. If you want to delete several files, tap on the 3 dots in the upper right corner, then tap on "select". Now tap on the squares in front of each file you want to delete. Afterwards, tap on "Delete" in the bottom left corner.