According to Derrida in On Grammatology, the entire Western civilization - culture, science, philosophy - was influenced by phonetic writing (alphabet) . Derrida opposes the concept of writing (and the grammatology he created) to a logocentric (metaphysical) system of concepts (speech and word) based on identity and presence (if these mean nothing to you, read intro to Deconstruction first). Rather, non-metaphysical writing refers to difference and absence. Writing is a way of the existence of a language in which traces remain.
The trace for Derrida is the original meaning, something displayed in the letter, it does not depend on the method of writing. The trace refers not to presence, but to memory, it is the past, which was never present. The trace is an imitation of presence, a ghost, an illusion. The trace exists before any primary attitudes and oppositions. There are different types of footprint: “motivated” (memory of an external impression), “conditionally motivated” (a word denoting an object that was recently seen), with “lost motivation”, without any motivation at all (arche-trace). Associated with the trace is a sign that exists in traditional metaphysics. Typically, a linguistic mark arises as a result of a trace.
Writing precedes any given in a phenomenological sense and does not refer to presence (presence). Writing is initially involved in the game of traces (that is, multiple differences, references, erasures, absences) and represents a trace, however, writing is not a trace (a trace does not exist in itself). Writing carries a fundamental property of Derrida's ontology - the ontology of difference. The expression of the letter - the text - has a special meaning, being the main subject of analysis. Derrida's formula - "everything is text" - corresponds to another principle: "there is nothing outside the language."
Writing is not something external in relation to logos, truth and meaning, it does not carry a destructive function, but only a demonstration of the origin of concepts and their connections among themselves. Traditional metaphysics tended to belittle the role of writing.
Other concepts are associated with writing, first of all "arche-writing", the original letter, which is a necessary condition for all forms of writing.
In later works, Derrida rarely used the concept of "writing", but it remains as a fundamental principle.