In 1943, after 23 years under French rule, Lebanon gained independence. Its new leaders established the National Pact, which allocated government power among the major religious groups. This independent Lebanon became a global destination, earning the nickname 'Paris of the East' or, due to its ski resorts in the Mount Lebanon range, 'Switzerland of the East.'
In 1971, the Palestine Liberation Organisation (PLO) moved its headquarters from Jordan to Lebanon. Hezbollah later emerged as a response to this, with Israel's crossborder interventions to combat the PLO further execerbating the situation. The presence of these armed Palestinians, especially the PLO, created conditions conducive to Hezbollah's rise. Other factors also played a role, including Israel's subsequent invasion and increasing Iranian support with its anti-Israel stance but tit was armed Palestinian threat that kicked things off. It could be said that without Israel, there would be no PLO, creating a 'chicken and egg' scenario.
Edit: Also worth noting that in July 1971, the PLO was expelled from Jordan following a Jordanian civil conflict known as Black September - Jordan kicking the PLO out.
From 1967 to 1970, the PLO engaged in a war of attrition with Israel while based in Jordan. During this period, Israel conducted raids on PLO camps, and the PLO responded with artillery attacks on Israel. The PLO moved the problem from Jordan to Lebanon.