Using the high-resolution photosphere and chromosphere observations made by the 1 m New Vacuum Solar Telescope, we studied the granular-scale magnetic flux emergence occurring in emerging active region NOAA 12579. Supplementary observations are also provided by the spacecraft Solar Dynamics Observatory. The studied granular-scale flux emergence took place at two different locations. One is completely embedded in the unipolar region of the following sunspots (Case 1), while another is located at the central part in the active region (Case 2). We find that both cases initially emerge from a dark patch like a wide intergranular lane, but showing the different subsequent features. In Case 1, the emerging granule grows in an elongated feature and reaches its maximum size of almost of 5 '' x 3 '', with an elongated speed of about 2-3 km s(-1). An eruption (i.e., surge) with bright footpoints is observed after the emerging granule reaches its maximum scale. There is a time delay of more than 10 minutes between the appearance of the abnormal granule and the H alpha surge. Furthermore, its footpoints are clearly rooted at the intergranular lane. We propose that the eruptive surge could be triggered by the reconnection between the emerging magnetic flux and the preexisting ambient field, leading to the localized heating and bidirectional flows. In Case 2, the granular cell emerging is simultaneously associated with bright points with opposite magnetic polarity, showing the separating motion between them and a bunch of newly formed arch filament systems. We infer that the bright points are due to the strong-field magnetic concentration in the dark intergranular lanes rather than the instantaneous Ellerman bombs.