(noun)
(American) broadly, a wide road that is open on both ends, often being part of a grid-like arrangement of roads;
e.g. This avenue of the city has many famous restaurants on it.
(noun)
(British) a walking path, driveway, or road, often planted with trees on either side, typically leading up to a building that is located off the main road;
e.g. We walked up a broad avenue to approach their house.
(noun)
figuratively, a channel or way of making progress towards some outcome, pursuing a particular aim, or approaching a problem;
e.g. This is the most feasible avenue of thought to pursue for resolving their dispute.