In addition, the lights are generally lit in the synagogue, often as part of a community celebration. Many synagogues have large and elaborate chanukiyyot, often donated by generous congregants who sometimes even commission a specially designed and crafted chanukiyyah.
Kindling the lights in the synagogue is partly in order to recall the original miracle of Chanukah, which involved the national house of worship (this is the view of the Mishnah B’rurah); partly to accommodate travellers who are away from home (Shulchan Aruch, Orach Chayyim 269); partly in order to increase the publicising of the miracle (pir’sum ha-nes).
One of the differences between the domestic synagogue custom is that in the latter, the lights are often re-lit in the morning. This may be because security sometimes dictates that the chanukiyyah is not left burning when the synagogue is locked up at night.
Some say that it recalls the practice in the Temple, where the staff could kindle lights in the morning.
Homiletically one could say that the Chanukah message applies both when the day is dark and the world needs to maintain its faith, and also when the day has dawned and the status quo needs to be zealously guarded.