Does terrain provide a defense bonus?

There are no terrain bonuses in Fire Emblem Heroes.

The only affect the terrain has in this mobile game is for movement, below is a quick summary:

Standard unit movement:

Flyers: 2 spaces
Calvary: 3 spaces
Infantry: 2 spaces
Armoured: 1 space

The terrain affects the units accordingly:

• Plains: Movement is normal
• Forest: Does not affect Flyers or Armoured, Infantry take 2 units of movement to enter, Calvary cannot enter.
• Mountain: Only Flyers may enter
• Water: Only Flyers may enter
• Walls: No units may enter
  (which is also different from past FE games where Flyers could fly over)

As of version 1.3.0, there are now defensive terrain bonuses for the defensive maps. According to this article, these spaces reduce incoming damage by 30% of the unit's Def/Res.

These new maps include defensive terrain. A Hero on a defensive terrain tile receives a damage reduction of 30% of their Def or Res.

For reference, this is what this terrain looks like in-game: