Full array means that the whole screen is covered with backlight led as compared to edge lit where they are only at the edges and a special reflective panel is used to reflect light from these.
Problems with edge lit led. In dark scenes there is backlight bleeding at the corners as well as problems with uniformity with some regions being slightly brighter.
Local dimming in full array backlight means that the backlight turns of in the regions where absolute black content is being portrayed which in turn increases contrast however these arrays have problems like blooming which increases the brightness of the contents around the edges of the dimmed area.