This is about undoing the opposition between speaking and writing, to put it simply. Derrida takes the notion that when you speak, there is a presence of meaning in your words, there are thoughts behind them that infuse them with this meaning (speech is hearing someone's thoughts); and then in writing there is a separation between meaning and word (because the writing has separated it from the person talking). Because neat oppositions like this are like waving a red flag at Derrida (well, was), he wrote a book called Of Grammatology dealing with it.

This book is the beginning of a type of philosophical and literary criticism called "deconstruction" (a termn Derrida coined in translating Heidegger, but that is a whole other can of worms), and deconstruction is precisely about undoing such simple oppositions (man/woman, mind/body, speech/writing, good/bad &c) by showing how they are dependent on each other. In such a set of oppositions, presence/absence, presence is valued above absence, which means speech is valued above writing -- as being more authentic.

If speech is a thought given out loud, it is a copy of thought; and this relegates writing to the position of a copy of a copy. It is therefore further from the "centre" of the thinking individual. Now, anything sporting a centre is bound to draw Derrida's attention (he likes pushing and prodding them).

The gist of what Derrida argues in Of Grammatology is that speech, like writing, is based in language, and language comes from outside the individual: it is communal, something shared, and therefore not something that can spring from the individual to perfectly express his thoughts (and by extension his being/his presence). Speech, because it is formulated in language, is already a form of writing. It cannot, therefore, convey the undiluted presence of the person speaking.

Oversimplified, but I hope it makes sense.

Edit: of course, he attacks "the metaphysics of presence" in a whole lot of different ways -- the speech/writing one is just one avenue, but it seemed the most relevant one, and it is the easiest one to understand.