Italy as a proportional representation electoral system with a minimum threshold of 4% in the House and 8% in the Senate (at the Regional level), therefore there is a multitude of smaller parties represented in parliament (as long as they obtained at least a percentage of votes above the threshold).
There are 630 Representatives in the House (House of Deputies) and 315 Senators in the Senate.
These are the main parties now represented in the current parliament (in order of size):
Partito Democratico (309 Reps, 113 Senators). This is the largest center left party and currently the majority party. The former Mayor of Florence, Matteo Renzi, leads the party and is the current Prime Minister of Italy. He's a centrist and moved the party decidedly to the center, much like Bill Clinton and Tony Blair did in their equivalent parties in the US and UK. It's a party that very closely resembles the Democratic Party in America, especially under Renzi's leadership (it used to be a bit more to the left before he took over).
Movimento 5 Stelle (5 Star Movement)(91 reps, 36 sen). It's a left wing party founded by a comedian (Beppe Grillo) who captured a lot of protest vote at the last election. They refused to participate in Renzi's government and sit with the opposition. They somewhat resemble the Occupy Wall Street movement in America. Its symbol is a 'V', in fact the name is written MoVimento, with a capitalized V in the middle. The V actually stands for "Vaffanculo" (I'll spare you the translation), the motto adopted by Beppe Grillo at his rallies. In 2007 Grillo called for a nationwide rally against party politics and career politicians called "the Vaffanculo day" or "V-Day".
Forza Italia (Go Italy) (70 reps, 64 sen). It's the main center right party founded by Silvio Berlusconi, its supreme leader. It has lost a lot of seats at the last elections. It resembles a moderate wing of the Republican party in America. Silvio's latest idea this week, is to rename it "Republican Party of Italy" and adopt the GOP's elephant as its symbol. This party is currently on the opposition.
Nuovo Centro Destra (New Center Right) (27 reps, 31 sen). A slightly right of center centrist party born from the split between Berlusconi and his former partner Angelo Alfano. This party chose to be in the governing coalition in support Renzi's government and Alfano is Renzi's Minister or the Interior.
Scelta Civica per l'Italia (Civic Choice for Italy) (25 reps, 0 sen). Founded by former PM Mario Monti, is a left of center centrist party currently part of the governing coalition led by PM Renzi.
Sinistra, Ecologia, Liberta' (a.k.a. SEL) (25 reps and 2 sen) is a left wing party (as the name implies) that chose to oppose Renzi's coalition from the left. It was founded by former left wing Democrat Nichi Vendola, the Governor of Apulia.
Lega Nord (Northern League). (17 reps 12 sen). It's a right wing party that in many ways resembles the Tea Party in America. They are for lower taxes, stop to immigration and repatriation of immigrants, Anti islam, Anti-gay movement, and in the past they advocated the Secession from the south and those lazy Southern Italians. Now they are willing to compromise on seceding from the South if they can simply kick all the Muslims and the gypsies out of the country. Its historic leader is Sen Umberto Bossi. It's current leader is Matteo Salvini (aka the other Matteo, as opposed to Matteo Renzi). One of its party leaders is Calderoli, a hard line physician who likes to take his pig on a leash for a walk to locations where local Muslims plan to build mosques.
In addition to the above there are 28 more parties none of which have more than 10 parliament members between representatives and senators.