Travian is a real-time game. Troops and merchants must travel from one spot to another, and this process takes actual time. The movement speed of an attack, a reinforcement, or a merchant determines how long you must wait for the action to occur.
Travian's game world consists of "fields" upon a toroidal board, partitioned using a Cartesian coordinate system. In simpler words: every field has an "X" and a "Y" coordinate, and the coordinates wrap around at the borders. Coordinates in Travian are written in the form (X|Y). (0|0) is the center of the board (and is always occupied by a Multi-Hunter village); (400|0) is on the far eastern edge, which wraps around (is adjacent to) the far western edge at (-400|0). Likewise, the northern edge is (0|400) and the southern edge is (0|-400), and this border also wraps around. (400|400) is the location of the Natars' capital village.
Villages and oases reside on this game board, at fixed coordinates. (Villages can be created and destroyed; oases are pre-allocated at world generation time.) The distance between two villages, or between a village and an oasis, is determined by applying the Pythagorean theorem to the coordinates. For example, consider a village at (23|-17) and a village at (-3|4). The horizontal distance between them is 26 fields (23 minus -3), and the vertical distance is 21 fields (4 minus -17). By the Pythagorean theorem, the distance between these points is sqrt(262 + 212) or about 33.42 fields.
An attack, reinforcement or merchant traveling this distance will do so at some specific movement speed, expressed in fields per hour. For example, a Teutonic merchant moves at 12 fields per hour. The trip from one of these villages to the other will take sqrt(262+212)/12 or about 2.79 hours. A merchant must also return, and this return trip will take the same amount of time. Travian will express the travel time, or the remaining time to arrival, in hours:minutes:seconds format. Since this trip really takes sqrt(262+212)/12*3600 or 10026 seconds, Travian would express this as 2:47:06.
A Gallic merchant moves at 24 fields per hour, so it would require sqrt(262+212)/24*3600 seconds, or 5013 seconds, or 1:23:33 for a Gaul's merchants to make this trip.
Movement speed of troops (both attacks and reinforcements) is also affected by the Tournament square building.