Florakis was born on July 20, 1914 in the Paliozoglopi village, located near Agrafa in the Itamos municipality, Karditsa prefecture, Greece. He joined the KKE, in 1941. A partisan during the resistance to the Nazi occupation in World War Two, Florakis was on the losing side of the Greek Civil War and subsequently left the country.
He returned to Greece illegally in 1954 and was arrested. During his life he spent 18 years in detention or jail - including being put in internal exile by the Greek colonels at the start of the 1967-74 military dictatorship.
First elected to parliament in 1974, Florakis led KKE as its general secretary from December 20, 1972 until 1989, when, though still fit for the job, he announced his decision to step down from the party's top post and proposed Grigoris Farakos as his successor.
Florakis did not retire from politics, however. In the same year he retired from the leadership of the KKE, he was approved as the president of the newly-founded Synaspismos or Coalition of the Left. Synaspismos was an attempt to reconcile Greece's two main communist factions, which arose in 1968 out of the Soviet intervention in Czechoslovakia that crushed the Prague Spring. That show of brute strength led many Greek communists to break with the Moscow-oriented KKE and to follow the nascent Eurocommunist path, which favoured national agendas and a more democratic road to socialism.
Synaspismos was created partly at the instigation of Florakis, and drew members from both the KKE and the Euro-communists. It also became an umbrella for other leftist groups and disaffected supporters of the Panhellenic Socialist Movement of Andreas Papandreou, which lost a general election in 1989.
In 1991, as it became increasingly clear that Soviet communism would not last, a rift arose within the KKE between those who supported continuing efforts towards a reconciliation with the Euro-communists through Synaspismos, and traditionalists who felt that communism was threatened internationally and favoured a return to ideological roots. Florakis sided with the latter and at the 13th KKE conference in early 1991 - even before the fall of Mikhail Gorbachev and the dissolution of the Soviet Union - the party officially withdrew all support from Synaspismos and Florakis was elected honorary president of the KKE.
Florakis died of heart failure at his home in Athens on May 22, 2005. Florakis' body lay in state at the KKE headquarters in Perissos on May 24-25 where thousands of party members and sympathisers queued to pay their respects. Party leader Aleka Papariga addressed a civil funeral on the evening of May 25 which was attended by the President of Greece Karolos Papoulias, prime minister Costas Karamanlis, parliament speaker Anna Benaki-Psarouda, opposition PASOK party leader George Papandreou, Left Coalition leader Alekos Alavanos, Cypriot communist party AKEL leader and Cyprus parliament speaker Dimitris Christofias, many ministers and MPs and other dignitaries. He was laid to rest on May 26 at the Agios Ilias cemetery in his native village.