The zombie will walk over the mesh, up and down. The navigational mesh calculates walkable areas on the terrain/mesh. If a hill is too steep it’s considered unwalkable for example. So the navmesh is a means of calculating the shortest path considering terrain and obsticles.
Without a navmesh, your zombies would attempt to simply choose the shortest possible direction to reach you. They would fall over cliffs or end up being blocked by buildings that turned out to be in the way.
The navmesh calculates a walkable map so a character can determine a “safe” path to it’s destination. Sort of what roads are to humans, as long as you keep following the road to where you’re going you can be (reasonably) sure you won’t end up in a mountain wall, building or an ocean.