What do the poems "The Songs of Innocence" and "The Songs of Experience" by William Blake mean?
"Songs of Innocence" and "Songs of Experience" are groups of poems published by William Blake in his book, Songs of Innocence and Experience, so your question really concerns a collection of many poems. What makes these poems really interesting is that they show the contrasts in human nature, in life, and in the very nature of God. In other words, they are poems of "opposites."
Perhaps the most famous of the Songs of Innocence is "The Lamb" which presents God as a gentle and loving presence. The opposite poem in Songs of Experience is "The Tyger," in which God is presented as a savage and fearsome force. Taken together, "The Lamb" and "The Tyger" both examine the nature of God, but each poem arrives at a different truth. God is a mystery to us. The Songs of Innocence are positive, affirming, and hopeful; the Songs of Experience are dark, gloomy, and sometimes quite poignant.
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.