der Anbau
cultivation
The systematic planting and care of crops in agriculture or in the garden.
Der Anbau von Biogemüse wird in der Region immer wichtiger.
The cultivation of organic vegetables is becoming increasingly important in the region.

cultivation / extension
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cultivation
The systematic planting and care of crops in agriculture or in the garden.
Der Anbau von Biogemüse wird in der Region immer wichtiger.
The cultivation of organic vegetables is becoming increasingly important in the region.

The word is derived from the verb 'anbauen' (to cultivate / to add on). The prefix 'an-' and the verb 'bauen' (to build, in the sense of 'to construct' or 'to cultivate') explain both meanings: you build something onto a house, or you grow plants in a field.
Wir wollen nächstes Jahr Tomaten im Garten anbauen.
We want to grow tomatoes in the garden next year.
You can tell which meaning is intended from the context. If it is about plants, vegetables, fruit, or agriculture, the first meaning is intended. If it is about houses, rooms, or architecture, the second meaning is intended.
Der Anbau von Wein hat hier eine lange Tradition.
The cultivation of wine has a long tradition here.
In an agricultural context, 'Anbau' (cultivation) is often combined with 'von' (of) and the type of plant. Common adjectives are 'ökologisch' (ecological/organic), 'biologisch' (organic), or 'traditionell' (traditional).
Der ökologische Anbau von Gemüse ist uns sehr wichtig.
The organic cultivation of vegetables is very important to us.
When an extension to a building is meant, the preposition 'an' (to/on) is almost always used with the accusative or dative to describe the connection to the main building.
Wir planen einen Anbau an das Wohnhaus.
We are planning an extension to the residential building.
culture
'die Kultur' and 'der Anbau' can both have to do with crops in agriculture. In this area, 'Kultur' more often means a cultivated plant species or the technical field of planting. 'Anbau' describes the work more directly: you plant and care for something so that it grows. In everyday language, 'Anbau' usually sounds more natural, for example with potatoes, wine, or vegetables. 'Kultur' is heard more in technical language or when talking about specific plant cultures.

Der Anbau von Tomaten braucht viel Sonne und regelmäßig Wasser.
Growing tomatoes requires a lot of sun and regular watering.
Auf dem Feld wird dieses Jahr eine neue Kultur getestet.
A new crop is being tested in the field this year.