What immortal hand or eye, Could frame thy fearful symmetry (lines 3-4)
Blake thought that the immortal part of a person, the divine part, was the poetic imagination (among some other things). The "hand" can be a metaphor for the creative ability of a person. The eye is, of course, vision in the standard sense, but also vision in the more mystical sense of seeing more than what’s in front of you. So, bringing all these together, the "immortal hand or eye" can be read as the mystical, creative vision of the poet’s imagination! Pretty cool, huh? With the second line, the heart of the question, the speaker could be questioning the ability of the poet’s creative vision to "frame," or contain the power of the Tyger. This leads into all sorts of exciting interpretations once you bring in stuff about what the Tyger might mean (God, the divine in general, the sublime, etc.). At its heart then, these lines question the ability of art itself to capture or communicate certain subjects!
On what wings dare he aspire? What the hand, dare seize the fire? (lines 7-8)
If you read "he" as the artist or poet, and the "fire" as the essence of the Tyger (or of the divine), then "seiz[ing] the fire" is the poet capturing those elusive things. So, the speaker questions who "dare" seize these things that, he thinks, are way out of the poet’s league. Also, the "wings" the speaker refers to may be the same "hand or eye" of poetic creation and vision that appeared in the above quotation (lines 3-4). Thus, he might be saying, "Who thinks he has the ability as a poet or artist to actually capture something so out-of-this-world as the divine?! Who do you think you are?"
Did he who made the Lamb make thee? (line 20)
This one’s tricky, so bear with us. The connection for this quotation requires a little research, but that’s what we’re here for. If "he" refers to the artist, and "thee" refers to the Tyger, then this line may be about creating poetry in general. How, you ask? Well, "The Lamb" is another poem by Blake, which he penned five years earlier, and "The Tyger" is the poem you’re reading right now. So, "he who made the Lamb," might be "he who wrote ‘The Lamb’"; and "thee," might not just be the Tyger, but "The Tyger." Following? The line might refer to the poems "The Lamb" and "The Tyger." Put another way, "Did Blake, who wrote ‘The Lamb,’ write ‘The Tyger,’ too?" The question becomes, then, why would Blake, who obviously wrote both poems, include a question as to whether or not he actually did? This is where the interpretation opens up. It could be because he’s questioning whether it is actually he who is writing them – perhaps it’s a higher power, or some force beyond him. There are parts of Blake’s other work where he claims to not have control over his arm, and that something or someone is writing through him. But perhaps it’s not so supernatural, maybe it’s his very imagination that is creating these amazing worlds and creatures on the page – how many times have you had a dream that seemed way beyond what you could ever think up while awake?