The tiger and the elephant skin symbolically signify his ability to control and transform animal nature. The trident represents the three qualities, namely sattva, rajas and tamas. The damru denotes his connection with the primal sound AUM, the creation of alphabets, languages, grammar and music. His long matted hair denotes his spiritual life and his great powers. It is also compared to the night sky. He wears a garland of snakes around his neck. Sometimes we see more snakes: one across his body like a sacred thread and two acting as bracelets around his muscular hands. The snakes symbolically represents his control over desire and sensuality. Sometimes in his ferocious aspects, he is shown wearing a garland of skulls. The crescent moon adorns his hair like a silver diadem. And the Ganges flows from his head down into the world below.

Though he is an ascetic, he lives with his family. He is very fond of his consort, Parvathi, whom he married after subjecting her to a lot of tests. While Vishnu is shown as being served by Lakshmi sitting at his feet, Siva and Parvathi are being shown as equals sharing the same seat on the snowy heights of Kailash.

Parvathi is literally described as his better half sharing half of his body. This earned him the title ardhanariswara (half female half lord). Normally we find her always by his side, especially when he is seated in Kailash, sharing with him all the honors that he receives. 

He seems to dot on his two children, Skanda or Kumara and Lord Ganesha or Vinayaka. The Bull Nandi is his vehicle. Nandiswara is humility personified. He is very knowledgeable also. Nandi taught Hanuman the secrets of Vedas and lessons in humility!  Another important member of his retinue is Bhringi, the zealous devotee who was not inclined to worship anyone other than Siva and refused to worship even Parvathi, till he was made to realize his mistake. Although a mountain dweller, he is not attached to anything and true to his ascetic nature, keeps wandering from place to place. Mount Kailash is his abode, where live his family, his devotees who attained liberation and his great army of goblins, imps and ghosts.

Symbolism

Siva symbolically represents the tamasic quality. Because of this he is called pasupathi, (the lord of the animals). His body color which is white, denotes his purity (sivam) and association with the snowy mountains. His three eyes represents the three worlds, the sun, the moon and the earth, the three paths of liberation and the triple nature of creation. The third eye is actually the eye of wisdom or occult knowledge. The moon that adorns his head represents the movement of time and also his cosmic proportions. With the the moon there, his head becomes the night sky, for which he earned the name Vyomakesa (one who has the sky or space as his hair). His association with the moon is in contrast to Vishnu who is associated with the Sun as a solar deity. The moon also symbolizes his association with the occult and the tantras. 
Siva is generally a seated yogi, a posture with which most Hindus are familiar. However we also come across Siva as nataraja or tandavamurthi in a dance posture. With his hair flying in all directions and hands and feet in dynamic motion, the image of nataraja is a symbol of harmony and rhythm. Among the objects which are associated with him popularly, apart from the trident and the Damaru, are battleaxe (parasu), rosary (aksamala), pasa (noose), khatvanga (magic wand) and khadga (sword).

Aspects of Lord Siva

Siva is known by several names and worshipped in various forms. We are mentioning below some of his most famous aspects:
Panchanana Siva:  In some temples Siva is shown with five faces. Each of the faces has a name and represents a specific aspect. These five faces are  Isana, Tatpurusa, Aghora, Vamadeva and Sadyojata. Isana faces south east and represents Iswara aspect of Siva known as Sadasiva, or the Eternal Siva. Tatpurusha faces the east. He is Siva in his aspect as a deluded purusha or ego. Aghora  faces the south and represents the destructive and regenerative aspect of Siva that, like fire, first devours life and then prepares the ground for its renewal. Vamadeva faces north. He is healer and preserver. Sadyojata faces west and represents the creative power of Siva.
Anugrahamurthy: This is the milder or peaceful aspect of Lord Shiva when he is in the company of his beloved devotees or his family members. 
Ugramurthy: Also known as Raudra , Bhairava, Kankala or  Samharamurthy, this is the ferocious or angry form of Siva, generally associated with the events during which Siva assumed his terrible form to slay the demons or the wicked.

Tandavamurthy:  Lord Siva is a master of dance forms. He is the author of all dance forms. The science of dance ( Natyasasthra) dealing with the 108 types of classical Indian dance forms said to have originated from him just as all the yogic postures. In case of  Lord Siva all dance is a form of expression, which he uses either to relieve the tensions in the world or alleviate the sufferings of his devotees. Sometimes he also entertains the gods or his wife or his devotees with his dance. About nine forms of Siva in dancing mode are described, of which the most popular form is Nataraja (the king of dance). Though we have a number of icons of Siva as Nataraja, he is rarely worshipped in this form either in the temples or in the households.

His other dance forms include, Ananda-tandava-murhty, dancing in a pleasant and cheerful mood, Uma-tandava-murhty, dancing in the company of Parvathi, Tripura-tandava-murthy, dancing while slaying Tripurasura and Urdhva-tandava-murhty, dancing in the air.