Why is the current unrest in the Arab world called the "Arab Spring"?

Solution 1:

According to this news article, the term is a reference to older revolutions:

Talk of an Arab revolution gave way to the adoption of the term "Arab spring" to describe developments. This has echoes of the "Prague spring" and other eruptions in Eastern Europe, which did not succeed in throwing off the yolk [sic] of Soviet domination until the collapse of the USSR.

The Prague Spring was a revolution in Czechoslovakia, which began in January of 1968. It was "Spring" because it included a series of reforms (where Spring is known as the season of new beginnings). The name of this revolution has also influenced the naming of others:

A decade later, a period of Chinese political liberalization became known as the Beijing Spring. It also partly influenced the Croatian Spring in Yugoslavia.[68] In a 1993 Czech survey, 60% of those surveyed had a personal memory linked to the Prague Spring while another 30% were familiar with the events in another form.[69]The Vatican' s semi-official newspaper L'Osservatore Romano referred to the regime changes taking place in North Africa in 2011 as "Arab Spring"

Solution 2:

In this case Winter (or perhaps ice and snow) is being used implicity as a metaphor for a society ruled by opression with little freedom. Thus "Spring" is indicating that the opression is melting away like the ice thawing in Spring.

As simchona correctly indicates, the metaphor was first used to describe the brief period of reforms tried out by Czechoslovakia. It was particularly apt in their case, because, like the real season, it came for a while then went away (thanks to Soviet tanks). Note that they even had their own self-immolating martyr.

Hopefully in the Arab's case, the Arab Spring will instead move on to a long summer. Inshallah