The Kerala state is densely populated because : 
1. The Kerala receives more amount of rainfall which helps in livelihood. 
2. Agricultural process will be more here, hence the farmers cultivate the coconut trees here hence the labors for agriculture are more. 
3. one among the western coastal plains part in the the Kerala i.e. Malabar coastal line hence the silt deposit will be more hence the agriculture and even the agricultural process can be more here.