Why do you think gardens have always been an intrinsic part of European culture?

In European culture, gardens have historically served a purpose that is two-fold: necessity and art. While in some instances separate, these two primary reasons for cultivating gardens have become interwoven over time and across cultures in Europe, becoming an essential and defining element of overall European culture.

Necessity

Gardens, in any location, originally arose out of necessity. Agriculture, including the cultivation of crops, vegetables, and herbs (both medicinal and as a source of food), has been, and continues to be, an integral part of human life since the transition away from a hunter-gatherer lifestyle. Though difficult to define, a garden certainly encompasses this necessary portion of human survival. Because of this, gardens have been present in a utilitarian form across the centuries, including in Europe.

A monastic vegetable garden
http://irisharchaeology.ie/2012/06/10000-years-of-history-the-irish-national-heritage-park-in-photos/

Art

It is in human nature to be expressive, with these expressions taking on a multitude of forms. In Europe, through the influence of numerous cultures and influences, from the Greeks and the Romans to the Medieval Era of Europe and onward, gardens have taken on the role as both a location for culture and art (such as with the concept of “otium” in Roman culture), and as their own expressive art, often in conjunction with a display of wealth and power.

A Roman peristyle garden
http://blogs.getty.edu/iris/archaeologist-kathryn-gleason-on-roman-gardens/

Within gardens as works of art, religion, another essential cultural aspect of human life and history over time, has played a major influential role in the structure and prevalence of gardens. Gardens gained symbolism through religion, which resulted in increased use of gardens as artistic tributes and places of thought and worship.

A Medieval "hortus conclusus" religious garden
http://retrofantasy.missyeh.nl/blog/wp-content/uploads/2009/07/hortus-conclusus.jpg

Conclusion

I think that cultivation is a natural human inclination. This can take on many forms: cultivation of language, of art, or, keeping with the natural association, of gardens. Europe, as a melting pot of cultures and civilizations over time, has a rich mixture of culture influences, which are reflected in the diversity and prevalence of gardens as a form of cultivation and expression.

The following link is to a website highlighting in detail some of the important historic gardens in Europe overtime: 

http://cmsen.eghn.org/ethg.html