Lord Siva is know as Pasupathinath, the lord of all creatures. Being a lord of the animals he has complete control on their behavior. Since a snake is one of the most feared and dangerous animals in the world, the garland of snakes around the neck firmly establishes this fact even the snakes fear Him and remain under his control.
The snake stands for all the evil and demonical nature in the world. By wearing the snake around his neck, Lord Siva gives us the assurance that no evil can touch us or destroy us once we surrender to him, seek his protection and worship him with deep devotion.
The snake also stands for the power of kundalini, which is described as a coiled serpent lying dormant in the muladhara chakra of all human beings and descends upwards when one starts ones spiritual journey and becomes increasingly divine oriented. The snake around the neck of Siva conveys the meaning that in him the kundalini not only has arisen fully but is also actively involved in the divine activity by keeping an eye on all the devotees who approach Siva with their individual problems.
The snake also stands for all passions and desires. By wearing the snakes around his neck, Lord Siva conveys the message to all his devotees that He has overcome all desires and is in full control of Prakriti, or maya and its various machinations.