What do the poems "The Songs of Innocence" and "The Songs of Experience" by William Blake mean?

William Blake's two-in-one volume Songs of Innocence and of Experience bears a sub-title 'the contrary states of human soul', the state of Innocence being seen as contrary to the state of Experience. Blake's presupposition is that progression is possible only through contraries. Innocence is associated with childhood, while Experience is associated with adulthood.

'The Lamb' is a theme poem of the section dealing with Innocence, whereas 'The Tyger' is a theme poem of the section dealing with Experience. In 'The Lamb', a child speaks to a little lamb, questions if the lamb knows who its maker is. The child speaker then proceeds to answer the question: 'Little lamb I'll tell thee'. In his answer, the child and the lamb cease to be different entities and merge together into the holy iconography of Christ:

He is called by thy name,

For he calls himself a Lamb.

He is meek and he is mild,

He became a little child,

I a child and thou a lamb,

We are called by His name.

In 'The Tyger', Blake envisions an apocalyptic beast, both frightening and beautiful-- a 'fearful symmetry'. This is no familiar tiger, but a burning object of awe and wonder, a creature presumably made by the same maker as symbolic of the world of Experience.