The lion head symbol was introduced in 1986 as an alternative national symbol of Singapore. The lion head was chosen as a nice logo, as it best captures the characteristics of Singapore's reputation as a Lion City. It is used in less formal occasions mainly to promote Singapore's national identity. 
When it was first unveiled, some sections of the public felt that it should have been facing rightwards to represent a more forward looking nature. However, the original left-facing lion was maintained.
In the 13th-century Malay Annals, Sang Nila Utama, a prince from Palembang was shipwrecked and washed ashore to an island. There he saw a creature which he believed was a lion. So he named the island "Singa Pura" which means "Lion City" in Malay, from which the name Singapore was derived. 
According to the Singapore government:
The lion head symbolises courage, strength and excellence, as well as resilience in the face of challenges. It is in solid red against a white background - the colours of the national flag. Its mane's five partings represent the same five ideals that are embodied in the five stars of the national flag, namely democracy, peace, progress, justice and equality. Its tenacious mane symbolises the nation's single-minded resolve to rise to any challenges and overcome any obstacles. 
Extracted from Guidelines on the use of National Symbols: The Singapore Lion Symbol (July 1999) published by the Ministry of Information, Communications and the Arts: