Hezbollah is a large millitant group mostly based in southern Lebanon with a goal to resist Israel.
It had large popular backing when until around 2000, Israel had occupied southern Lebanon. It got a lot of support from the people on the street, and the governments of Syria and Iran.
It has also been involved in two conflicts with Israel since the Israeli withdrawal, but still enjoyed widespread support as "Legitimate resistance" and also for being a thorn in Israel's side.
The people of Syria supported Hezbollah almost totally, and this was helped by the fact that the regime also supported Hezbollah as its trump card to hit Israel should any hostilities arise with Israel or its allies.
The people of Syria gave them shelter and support.