This is the repeated use of the same letter at the beginning of, or within, words in close succession.

This can be used to emphasise words or phrases, or to add humour, or simply to make something sound more catchy or memorable. For this reason it is often used in football chants and nursery rhymes.

For example, tongue twisters use alliteration:
Peter Piper picked a peck of pickled peppers.

Often alliteration is used in newspaper headlines, or in adverts to create memorable catchphrases etc. Dependant on the letter used it can have a harsh, striking effect or a gentle, softening effect.

Another form of alliteration is Assonance, which is the repetition of vowel sounds within a word, so is a little more subtle, eg, Jony-Jo the pony, and he only eats lean meat

Finally, Consonance is another form of alliteration where the same consonant is repeated in close succession. eg pitter, patter or kissing Mississsippi on the lips.
(See my silly poem for an example of it's use.

These techniques can really help to make your writing more interesting to read; try practising them with the following ideas:

For example, Magical Martin, Brilliant Bradley etc
Notice how much better Brilliant Bradley is than, for example, Bouncing Bradley as the repetition of "Br" emphasises the alliteration even more.