Pests Of Basil

It appears that your basil is suffering from the feeding of slugs/snails (unless you see caterpillar poop), and a nutrient deficiency. We’ve included a link with info about slug/snail control and one about the needs of basil plants. The nutrient deficiency is either caused by a lack of nutrients in the soil (which may require additions of fertilizer) or too much water. Excess water damages roots (especially if temps are cool and/or coastal overcast conditions are frequent) so that the roots can’t function to take up nutrients, even if you add fertilizer. Basil performs best in moderately moist, well-drained soil, and may require some fertilizer in poorly managed soils. http://www.ipm.ucdavis.edu/PMG/PESTNOTES/pn7427.html
http://bonnieplants.com/growing/growing-basil/