Alliteration is the repetition of a consonant sound, within a line of poetry. Similarly, assonance is also when a sound is repeated within a line of poetry, but it is the repetition of a vowel sound.
In William Blake's "The Tyger," the alliteration and assonance serve to make specific lines of the poem stand out. For example, the first line is alliterative in two places: "Tyger! Tyger! Burning bright." Here both the "t" and the "b" sound are repeated. Essentially, the "t" and "b"are rather harsh sounds. The accompaniment of the exclamation point adds to the intensity of the first line. It is not only seen as yelling, it is seen as speaking down at the tiger as well.
Assonance, given the repetition of a vowel is heard, is much softer. It seems that the speaker of the poem wanted to get the tiger's attention, and then, once received, decided to change his (assumed given the gender of the poet) tone (as if the tiger turned and glared at the speaker).
The speaker's questions come from pure lack of knowledge. The speaker is questioning how the tiger, a creature of God, could be constructed by the same hands which made the lamb. This, too, adds to the back and forth nature of the alliteration and assonance (it seems the speaker is speaking loudly about the tiger and softly about the lamb).
The overall effect of the alliteration and assonance allow certain lines to stand out based upon how one reads the poem. At times, when the line is filled with assonance, the lines come out softer and more musical). When the lines are filled with alliteration, the lines are harsher and more demanding.