What is a lane?

Lanes are the main roads in game where people come and fight. Those are usually the larger roads on the map, where the objectives (like towers) stand, and where the monsters spawning in your base (creeps in Dota, minions in League of Legends and Smite) face the ones from the other team. Those are also the roads which are linking the two bases.

This term appears in many MOBA games. As you mentioned, there is Smite, but that's also the case for Dota or even League of Legends (what we call "Top", "Middle" and "Bot").

For League of Legends, these are the lanes :

This is the same concept for Dota :

For Smite, those are the larger roads on the left, middle, and right on this map :

The alternative paths that we can see on the maps are usually not called lanes. Those are just alternatives roads. Usually, that is what we call the "Jungle". There is also, in League of Legends and Dota, a road which divides the map in two diagonally : the "River". The traditional monsters of your team never use those roads.

Not all the maps necessarily have three lanes. For instance, the Howling Abyss map from League of Legends, or the Smite Assault Mode's map only have one lane. Another example is the Twisted Treeline map in League of Legends, which has two lanes (on the top and the bottom).

There are also maps without lanes. Smite's Arena Mode for instance does not have any. But most classic maps, where the goal is to take down objectives (such as towers) and go to the other player's base, contain at least one lane.

(Credits to League of Legends Wikia, Quora and Smite Academy for the pictures).

Lane appears in all MOBAs and is one of the main collision paths. Its the "road" where the mobs clash, where the towers are and where most of the fights are supposed to be (excluding jungle)

Disregard the tutorials, the maps there most of the time are not MOBA type but tutorial type, to teach you the basics of the game, rather than to put you and 9 other people (given most mobas are 5v5) in fights.