This was especially true in Athens. The woman of the house was responsible for the production of most, if not all, of the textiles needed by the oikos.* In richer households this mostly meant she oversaw the slaves who did the actual work of carding, spinning, weaving, etc. The majority of wives, however, did this work themselves with the help of other women (free and slave) in the household, though in households with enough people the highest status work, weaving, usually went to a higher status woman, leaving more menial tasks women of lower status. In addition to making most or all of the cloth needed by their respective oikoi, the free women of Athens were responsible every year for weaving the peplos worn by the city’s statue of Athena. Every four years they wove the peplos for the Panathenaea, which was large enough to be fixed to a ship as a sail.
Textile work was nowhere near so important to Spartan women. According to Xenophon, Lycurgus (supposed founder of the Spartan state) felt that slaves were capable of creating enough cloth for a household, freeing wives up to focus on running their households and making themselves fit mothers.** There is evidence, however, that Spartan free women’s work did include weaving. Weaving for ritual purposes was done almost entirely by free women. Unlike Athenian women, however, their reputations did not depend on their skills in weaving.
Textile work was the main part of women’s work elsewhere as well. It was important enough in Gortyn that the city’s law code stipulated exactly how much of what she had woven a woman could take with her when she divorced. In those cities for which we have archaeological evidence, Olynthos for example, the prevalence and locations of loom weights back up the assertions of literary sources. Nearly all Ancient Greek women were involved in the making of textiles, the only kind of women’s work that Greek men seemed to find productive.
*A rough translation of this word would be “household” or “family.” It was the basic unit of society in most Greek city-states.
**It probably helped that Spartan clothing was far less complicated and voluminous than Athenian clothing.
Lefkowitz, Mary R. and Maureen B. Fant, trans. Women’s Life in Greece and Rome: a Source Book in Translation. Baltimore, MD: Johns Hopkins University Press, 1992.
Plato, Republic 5.451-461e - Perseus
Plato, Laws 7.804-806c - Perseus
Hesiod, Works and Days 59-82 - Perseus
Xenophon, Constitution of the Lacedaemonians 1.2-10 - Diotima
Diogenes Laertius 6.96-8 - Diotima
Xenophon, On Household Management [Oeconomicus] 6.17-10 -Diotima
Occupations of Freedwomen. Athens (Lewis, Hesperia 28  208-38 - (Found in Lefkowitz & Fant (no.329), no link available)
Pausanias, Description of Greece 5.16.2-4 - Perseus
Pausanias, Description of Greece 3.16.1-2 - Perseus
Laws Relating to Women, Gortyn, Crete - Diotima
Pomeroy, Sarah B. Goddesses, Whores, Wives, and Slaves. New York: Schocken, 1995.
Pomeroy, Sarah B. Spartan Women. New York: Oxford University Press, 2002.
Nevett, L. C. “Gender Relations in the Classical Greek Household: The Archaeological Evidence.” The Annual of the British School at Athens 90 (1995): 363-381.