As Owlet explained, &c. is an abbreviation for "et cetera," and as The Soulful Ginger indicated, it was once widely used when signing one's name. European monarchs were especially prolific users of such a signature; their titles were so long that writing them out would take all morning, For example, Tzar Nicolas II's full title was
"We, Nicholas the Second, by the grace of God, Emperor and Autocrat of all the Russias, of Moscow, Kiev, Vladimir, Novgorod, Tsar of Kazan, Tsar of Astrakhan, King of Poland, Tsar of Siberia, Tsar of Tauric Chersonesos, Tsar of Georgia, Lord of Pskov, and Grand Duke of Smolensk, Lithuania, Volhynia, Podolia, and Finland, Prince of Estonia, Livonia, Courland and Semigalia, Samogitia, Białystok, Karelia, Tver, Yugra, Perm, Vyatka, Bulgaria, and other territories; Lord and Grand Duke of Nizhny Novgorod, Chernigov; Ruler of Ryazan, Polotsk, Rostov, Yaroslavl, Beloozero, Udoria, Obdoria, Kondia, Vitebsk, Mstislav, and all northern territories; Ruler of Iveria, Kartalinia, and the Kabardinian lands and Armenian territories; hereditary Ruler and Lord of the Cherkess and Mountain Princes and others; Lord of Turkestan, Heir of Norway, Duke of Schleswig-Holstein, Stormarn, Dithmarschen, Oldenburg." 
The poor guy would've been lucky to remember half of the provinces over which he was lord, duke, or heir, let alone how to spell them or what order they came in. Plus, signing his name like that would have used up an extra roll of parchment each time. So instead, he often simply wrote, "We, Nicholas II, By the Grace of God, Emperor and Autocrat of All the Russias, King of Poland, Grand Duke of Finland, &c., &c., &c." 
Sometimes, although less commonly, the entire signature was replaced by &c. It wasn't used just in the Old English period, however - I first encountered it in high school when I began reading Romantic and Victorian novels like A Tale of Two Cities and Jane Eyre, where it is often used to extend lists or end letters.
P.S. My signature comes from Pride and Prejudice, in which Jane often concludes her letters to Elizabeth with "Yours, &c." I assume that here the "&c." cuts down a phrase like "Sincerely yours, with much affection, and wishing you the best." I don't have any evidence for that theory, though.