Essentially, the poet (or speaker of the poem) is posing a question: who could have created a beast as terrifying as the tiger? The language of the poem, however, creates a dreamlike symbolic backdrop for this question that is hard to explain definitively. In other words, you can say that the poem poses a question, but the poem means a lot more.

If we look at the poem more closely, perhaps we can see how meaning and symbol interact in this poem. The first stanza begins,

Tyger Tyger, burning bright,
In the forests of the night....

Here the poet is either addressing the tiger directly or imaginatively calling forth the image of the tiger. Either way, the word "burning" might refer to the tiger's bright color, but the image of the tiger on fire is something you might expect to see in hell. Similarly, the phrase "forests of the night" calls to mind an image of a dark forest illuminated by the terrible light of the tiger. It also suggests (perhaps) a kind of internal "forest," a place of mental or moral confusion. Either way, a forest at night is a place where people get lost and are potential prey for wild animals. It is a beautiful yet terrifying image.

What immortal hand or eye,
Could frame thy fearful symmetry?

This is the central question of the poem. Simply put, it means, "How could God create such a terrible thing?" The question also inverts the standard notion that beauty and goodness coincide. The "symmetry" of the tiger (symmetry usually being associated with beauty) is not good but "fearful." The implication is that this terror is part of God's "symmetry," the divine plan for creation. Additionally, the way the question is posed suggests a kind of challenge to God: the poet is essentially saying, "What sort of God could have done this?"

The next three stanzas essentially ask the same question over and over in different ways. The first two lines of the second stanza read,

In what distant deeps or skies. 
Burnt the fire of thine eyes?

The speaker asks where in heaven could God have found the inspiration for the fire in "thine" (the tiger's) eyes? Each question is a variation on this theme. These questions express a kind of heretical accusation toward God but also can be understood to pose questions about the nature of artistic inspiration (like where do crazy poems like this one come from?) and the act of physical creation. There is a sense in which Blake conflates God and artist—both are creators.

On what wings dare he [God/Poet] aspire?
What the hand, dare seize the fire?

"Fire" could be understood as the fire of the burning tiger, but it also refers to the fire of the forge, referenced later in the poem.

And what shoulder [of God], & what art [skill or technique]
Could twist the sinews of thy [the tiger's] heart?
And when thy heart began to beat,
What dread hand? & what dread feet? [the hands and feet of God]

Blake's conception of God is strikingly physical. In fact, he imagines him as a blacksmith. This is made explicit in the next stanza:

What the hammer? what the chain,
In what furnace was thy brain?
What the anvil? what dread grasp,
Dare its deadly terrors clasp!

God-as-blacksmith is a potent and complicated image. On one hand, there is a sense that Blake is admiring the terrible handiwork of God as master craftsman. On the other, the potent sensory details here, of God's hammer pounding out the tiger's body on a divine anvil, or God forging the tiger's brain in a divine "furnace," suggest a kind of hellish scene, even though God is supposed to be the king of heaven! Critics have also remarked on how these industrial images suggest an indictment of the Industrial Revolution, which was transforming England at the time of this poem's publication. Seen in this light, the tiger might mean England's terrible economic might. This surprising image of a hellish God making terrible creatures is explicitly called out in the next stanza:

When the stars threw down their spears
And water'd heaven with their tears: 
Did he smile his work to see?
Did he who made the Lamb make thee?

In other words, heaven was so shocked by the creation of the tiger that the stars themselves revolted. The speaker wonders if God took a secret delight in creating this monster.

That last question ("Did he who made the Lamb make thee?") refers both to Christ (the "lamb of God") and Blake's own poem "The Lamb," which celebrates the innocent purity of the lamb. This question rephrases the question from the very beginning of the poem in a more direct and pointed way. How could the same person who made the lamb also make the tiger? Or, to put it another way, how can the same God who makes goodness and purity possibly also create death, destruction, and sin?

The final stanza repeats the first (maybe another kind of "fearful symmetry"?) with the crucial change of one word; instead of "could frame thy fearful symmetry," the speaker says "dare frame thy fearful symmetry." This change signals that the poet, as a result of these reflections, has come to a conclusion: the creator of the tiger perhaps violated his own rules or plan, and this is a kind of betrayal, both of the poet and also of creation. How "dare" God do it?