I've broken this post down into sub-sections to help organize it.
Why now?As mentioned in an earlier post, this was triggered by instability. Greece attempted to elect a President, but could not find the needed votes in Parliament. Rather than keep trying, the sitting government called snap elections, believing it could win.
Now is also important in the big scheme of things. Additional elections this year include, but are not limited to Finland, the UK, Denmark, Portugal, Poland and Spain. Results of this election could have knock-on effects on each of these countries.
SYRIZAThe main Left-Wing party is SYRIZA, the Radicals. They are lead by Alex Tsipras, who has become a Europe-wide symbol of anti-austerity. They are a new party, only a few years old, and exactly who they are is still being established.
Originally running on rhetoric that they would take a hard line against Austerity, even if that means a default, the party now is running on a more 'moderate' platform, saying they want to re-negotiate the terms of the bailout, rather than pull out of it altogether.
New DemocracyThe current government, and the Conservative party, is ND. ND is one of the traditional 2 parties of the Greek 2 party system. The current ND government has been the one to administer the bailouts and the after effects of the recession. They are unpopular due to the Austerity measures.
For this reason, they are, in effect, the "Non-SYRIZA Party" and the "Pro-Austerity Party" For this reason, there is not much to say about ND beyond that if they are re-elected, we can expect things to continue as they have been.
Other PartiesThere are many other parties. The Communists (KKE) are openly Stalinist, while Golden Dawn (XA) are openly Fascist. Perhaps most notable however is PASOK, the former lead left-wing party. PASOK is in coalition with ND.
Other parties that could win seats include ANEL and Potami. The former is a right-wing anti-austerity party and could possibly sit with SYRIZA in a government.
There are concerns about XA. Polls currently show they will likely lose seats, and this is uniformly a good thing for everyone who is not racist.
European ReactionThe entire election, in terms of it's importance to the world, is how Europe reacts. Early in the election, all the sounds made by Europe (IE Statements from people like Merkel) were that there would be no change to the deals negotiated with Greece. That, however, has changed. More recent statements indicate that European nations may be willing to talk to Greece. Nothing is solid, some countries like Finland, which had it's own debt crisis, will only help on certain conditions.
Things will get complex if SYRIZA wins, and there will be many things to say, from many people, about many issues. If they do not win, there won't be much of anything going on.
If things go wrongGreece could leave the Euro. As outlined earlier, this could also lead to Greece leaving the EU, something that Tsipras does not want. Depending on how far in to a corner Tsipras gets backed, he may have no choice.
It's important to remember that no country has left the EU, nor is there any official method to do so. One country suddenly leaving may encourage others to do so as well, and this could lead to additional problems in the EU.
If things go rightThis could kick off anti-austerity politics around the world. Given the possible fall out of a "Grexit" Europe may weigh the options and decide that it is better to give them what they want. This could spark changes in Spain, where a party like SYRIZA currently leads the polls. Should Spain follow suit it would send a message that opposition to austerity is possible, and it could send a message to other parties and countries in Europe that they too can renegotiate their debts. This could even spread to elsewhere in the world, and have impacts at home. While it's a bit of a stretch to say "If SYRIZA wins, the NDP will win here" this is within the realm of possibility, depending on the circumstances.
SYRIZA has a real chance to make things better for the average Greek, and if successful, could prove to be a model for use around the world, and perhaps, something to finally use to solve income inequality problems.