From my experiences of playing the game I've come to the following conclusions with the tile ratings:
Fertile land is mostly random around the map, and when you have fertile land you get increases to grain, material, and essence.
I think that all fertile land starts with 2 grain, 2 material, 0 essence, then depending on the terrain nearby bonuses occur to the grain and material tile yields.
Forest, iron mines, clay mounds increase nearby material yields on the fertile land tiles.
Plains, wheat field (big bonus), twilight bees (big bonus), rivers increase nearby grain material yields on the fertile land tiles.
Crystal crags, shards give bonuses to the nearby essence on the fertile land tiles.
As for city bonuses to your cities, obviously building improvements on the iron mines, clay mounds, and lumber yards (for forests) increase your production, but not the material yield. Wheat fields, twilight bees, docks (for rivers) increase your food, but not your grain yield. Shards increase your mana, but not your essence yield.
Of course, all of these yields have randomness, and so the numbers vary from time to time, and I don't think there is a precise formulae for the actual tile yield.