When I over over arrows and paths, I see some numbers. What are they?

You have a certain number of "action points" you can use to initiate combat, spells, or move around.  These points slowly come back with time, although there are other special ways to get ap boosts.  You can increase maximum AP through the shop.

If you mouse-over an arrow and see numbers, that is the action point cost to make that move.  The first number is the base cost, and the second cost is the current viscosity add-on.  Very high base costs occur at gates and similar barriers.  Viscosity builds up to a maximum of +20 if the area is untravelled, but falls off as more and more people move through an area.  Even if this results in a negative number, it will still cost a minimum of 1 ap to make any move.

Other things not shown can also affect the AP cost of a move.  For instance, Cartography skills reduce it.  Land loyalty, which is gained by being in that specific land when the server hits 0:00, reduces movement cost in that land only.