The Coptic script takes its name from the Egyptian Christians, the Copts. Strangely enough, the word "Copt" was originally came from the Greek word "aiguptios", meaning 'Egyptian'. It was shortened to "guptios", then transmitted into Arabic as "qopt", and finally back into Egyptian as "coptos". As the name implies, the Coptic script represented the Egyptian language just as Egyptian hieroglyphics had done for 3000 years before.
The Coptic script was adopted from the Greek alphabet approximately around the 2nd century CE. The Copts adopted the Greek alphabet completely even though many of the Greek letters represent sounds that didn't exist in Egyptian. Instead they kept the extraneous letters for their numeric values. In addition, the Copts added 5 letters, taken from the Egyptian script, that represent sounds that don't exist in Greek. The final count of signs was 32, and neatly represented the Egyptian language at the beginning of the first millenium CE.
Unlike the three Egyptian that preceeded it, the Coptic script represents both consonants and vowels. This has helped scholars immeasurably in reconstructing the history of the Egyptian language as well as provide some insight into how Egyptian words were really pronounced.
The Coptic script replaced the Demotic as the commonly used script in Egypt. It eventually went out of fashion around the 14th century when Arabic became the predominant language in Egypt. The Coptic script and the language it represents were restricted to liturgical purposes in the Coptic Orthodox Church.
The following is the Coptic alphabet. The letters in blue denote the phonetic value of the letter, while the words in purple are the names of the letters.