I would never dare to think I have enough knowledge so as to freely talk about this issue and produce a meaningful article, but I will try to write down what I have understood so far (I already had to edit as I misunderstood some facts, thanks Louis!).
Lebanon and Syria have always been deeply interconnected. Both countries were part of the Ottoman Empire, both countries were under the dominance of France's colonization, both countries share an extremely complicated ethnic/religious division, and both countries political scenes still depend on the other's. More recently, Syria was a key player in the brokering of the 1989 Taif Accords putting an end to Lebanon's civil war, and its troops (and many authorities) stayed in the country (allegedly guaranteeing the non resumption of violence) until 2005, when the country's population unanimously demanded their retreat.
It all started in Tripoli, Lebanon's second largest city, next to the country's northern border with Syria, home to perpetual foes living in rival areas that have been subjected to regular skirmishes since 1975: the Bab-al-Tibbaneh neighborhood dominated by Sunnis and the Jabal Mohsen neighborhood dominated by Allawites. This time, the clashes started on 20 August for reasons still not 100% clear (some journalists believe the initial spark came from a fight between children, for example here). A Sunni sheik was shot there to death on Friday, an action that clearly led to the escalation of the heavy infighting between rival factions that has been miring the country over the last months, mirroring the neighboring country's main conflict (Sunnis against Shiite Allawites, even though other issues are at stake) in the city and its outskirts. This event adds to the sensible situation the Mediterranean country is facing, where the main fear is the waging of a new sectarian war. Last week, scores of Sunnis were kidnapped throughout the country. Moreover, the former Christian minister of information was arrested weeks ago on the grounds of having planned a campaign of terrorist attacks so as to sow discord. The fighting has already left behind more than 20 dead and dozens wounded so far.
The surge has been even felt in Beirut, where the roads to the airport were blocked by Shiite militias in retaliation for the murky killing of Shiite pilgrims (an Air France plane had to be surprisingly diverted to Damascus, where the crew had to ask the passengers for cash in order to pay the refueling allowing them to fly to Cyprus!).
A new terrorist group is to blame for a huge part of the mayhem: the key name to retain is Mujtar Al-Thaqfi. Their initial demand was the liberation of a Shiite leader, Hassan al Meqdad, that had been kidnapped by the Free Syrian Army, but some pundits believe this is only an excuse to export the war that is being already waged next door.
The situation of the refugees in the north of the country is faring worse by moments: both reports by the United Nations refugee relief agency and accounts by officials and workers in refugee camps consider the emergency relief efforts undertaken so far are inadequate and have underestimated the needs of the refugee population. According to U.N. figures, 36,000 Syrians have taken refuge in Lebanon since 2011. In addition, Lebanon still hosts more than 400,000 Palestinian refugees. And that inflow dangerously aggravates the sectarian infighting. The Lebanese Army is strengthening its presence in the north of the country, particularly in Wadi Jaled and Tripoli itself, areas that have become an habitual place of passage not only for refugees, but also for the main supporters of the Syrian opposition and rebels, foreign volunteers (some of them jihadists) whose aim is to fight in the ranks of the Free Syrian Army.
It all comes down to the maintaining (or not) of the fragile political and sectarian balance in Lebanon created after its bloody civil war. The Lebanese authorities are well aware of the threat. Lebanon's Prime Minister clearly stated all political parties are to be blamed for the recent events and its repercussions: "our top priority is nowadays to avert sectarian fights [...] but there is no doubt various parts are willing to drive Lebanon into conflict".
Fortunately, Hezbollah (a key ally of Syria, together with Iran) has apparently dissociated itself from the wave of violence. However, the Free Syrian Army has repeatedly accused the militia of having made brief incursions into Syria from the very first beginning of the uprisings with the aim of getting rid of rebels and steal their weapons.
The international community is already showing its concern. According to CNN.com, Jeffrey Feltman, U.N. under-secretary general for political affairs, told the United Nations Security Council during its monthly meeting on the Middle East that "the situation in Lebanon has become more precarious and the need for continued international support to the government and the Lebanese Armed Forces increasingly important", adding that "tensions over domestic and security concerns remain high throughout the country and are easily exacerbated by developments in Syria". Countries openly supporting the rebel cause, like Qatar, the Emirates or Saudi Arabia, have already asked their nationals to immediately abandon the country.
Thank God, optimistic views have also been expressed. One example is the pundit Rami Khouri: "both the government, backed by Hizbollah, and the security forces are adopting a more decisive approach than before, and therefore try to suffocate all significant signs of violence in the country".