Culture can be defined as the sum total of learned beliefs, values and customs that serve to direct the behavior of members of a particular society. Advertising, and more importantly great advertising, captures and defines the cultural moment when it:

Uses shared experiences

"We are more like our times than we are like our parents." It is well known that people born over a short and contiguous time period are bound together by their shared experiences during their 'coming-of-age.' These generational cohorts form attitudes towards products, music, money, sex etc. in their formative years and these core values are carried through life largely unchanged. (Meredith & Schewe, 1994).
When advertising is able to target these cohorts through their shared experiences it becomes as much a part of their culture. Generation X has been largely brought up on colas due to large scale commercialism by companies during their times using their music (rap, grunge, retro) and their experiences (proms, coming-out-parties). Even as they age, cola drinking will remain a part of their choices and cola advertising will be as ingrained a part of their culture as it is today, if it is still done right.

Uses shared Symbols & Values

Both culture and advertising are symbolic domains, and we attach meanings to these symbols. When advertising uses powerful symbols from popular culture that holds positive meanings for us, the ads and the products they sell become as much a part of our culture as these symbols. The legendary Nike and Michael Jordan campaign is a case in point. Nike share rose from 18% to 43% in just a decade and the commercials became a part of our list of most memorable ads. Michael Jordan was not only the most recognizable athlete in the world but also a hero to the young boys. He stood for the age old American values of achievement and success. Michael Jordan & Nike achieved what in ad parlance is known as STT or " spontaneous trait transference" from the endorser to the product and in the process Nike Ads defined the cultural moment. Thanks to the powerful symbolism of Air Jordan.

Becomes the Lingua Franca

While advertising and culture both share common language and meanings, there are times when it becomes the language and the meaning. It becomes the lingua franca for large segments of the society. "Whassup" from the Budweiser commercials is as much a part of our daily parlance as any of the learned greetings that we acquired as part of our enculturation. And so are other popular slogans like "Do the Dew", "Just Do it" and many others.
Advertising's power transcends boundaries and language barriers where it becomes a 'visual lingua franca.' Nike, Coca-Cola, Harley Davidson all form a world of symbols shared with the international youth culture. Consumerism helped largely by advertising is tying the youth around the world through a common appeal.

Defines new rituals & cultural roles

When advertising ads more meaning to our lives through adding customs and rituals it stays in our minds 'forever' and becomes an inseparable part of our lives. The De Beers "Diamonds are Forever" was not just an advertising campaign; it redefined the whole courtship and marriage ritual in America. Diamonds were just treated as an investment commodity and men gave everything from minks to automobiles, anything except for diamonds to express love. De Beers through their mushy, well targeted campaigns using poetic copy and classical music added more meaning to the values of love and commitment and a diamond engagement ring became a must for every American bride-to-be.
In fact in Japan where there are no elaborate wedding rituals, except for drinking rice wine from a wooden bowl, as many as 80% brides are wearing diamond engagement rings today (Twitchell, 2000).

Becomes a reflection of the individual

To understand advertising and culture, we not only need to study people and their environment but also people and their relationship with the products. To quote from the book titled 'The meaning of things"-Man is not only homo sapiens or homo ludens, he is also homo faber, the maker and user of objects, his self to a large extent is a reflection of things with which he interacts. (Csikszentmihalyi and Rochberg-Halton, 1981). Advertising thus is dealing with a fundamental aspect of human behavior, and integrating the consumer within a rich web of social status and symbolic meaning. Consider the relationship between a Harley possessor and his bike. It stands for everything that the owner does: freedom, individualism, pride of possession and much more. The individual reflection with a Harley becomes a mass expression with H.O.G. (Harley owner's group) and an entire group of people is ready to be identified through its association with a product.
All these processes do not work in isolation though, while a celebrity endorser can transfer certain relatable values to the product, similar values can be associated directly with the product through image advertising (like Harley-Davidson) and still be an ingrained part of our culture. One can only add that advertising has not only becomes a part of culture through different ways; it is barely distinguishable from culture today.

References:

Meredith, G. and Schewe, C. (1994). The Power of Cohorts. American Demographics. December: 22-31.

Twitchell, J.B. (2000). 20 Ads that shook the World. New York. Crown Publishers.

The Book of Gossage. (1995) Chicago. The Copy Workshop.