To max out your resources means to reach the greatest production possible for a city.
Maxing out resources in a capital city can be a long, painful, and expensive process that can leave you vulnerable to enemy attacks. If the player does not belong to a very large (perhaps the largest) alliance or if the player's city is not located very far from other large players the city is at risk of takeovers and farming. It is highly suggested the player use gold to speed up the process as some final upgrades without gold can take well over 300 hours to complete making it impossible (or nearly so) for this accomplishment.
This is not a guide on accomplishing a max out, but advanced information to educate you on what is a possible maximum level for each resource in a capital city. This information assumes you have gold and use it to complete upgrade tasks immediately.
In the following tables you will see how many granaries and warehouses are required to complete the maximum resource upgrade level, the maximum possible level will always be in bold italics font. Anything after that will require Great Granaries and Great Warehouses, if the required space is available.
As there are only twenty slots in a normal village, to construct Level 19 fields, it is necessary to demolish every other building to fit the 12 warehouses and 7 granaries. You cannot destroy the main building as it is required to build a warehouse, granary, or marketplace.
With the 3.5 update to Travian, it is possible to upgrade your fields further. The Builder's Sketch artifact enables you to build the Great Warehouse and Great Granary in that village. As these buildings have triple the capacity of their regular counterparts, it is possible to build Level 20 Crop fields using seven Great Warehouses and two Great Granaries. Supposedly fields can be upgraded indefinitely on the capital in 3.5.
The following table shows how many Great Warehouses and Great Granaries are required to build up different crop field levels.