Culture spreads via a process anthropologists call cultural diffusion. Simply put, culture spread when two different cultures have close interactions with one another or when one nation conquers another. When the latter happens, it is called forced cultural diffusion.
In the past, cultures spread slowly through the everyday interactions of people. Common interactions included trading, marriage, war, travel and religious missions. In this way, cultural ideas and customs spread very slowly. A new wife would introduce new foods to her husband's family or warriors would take some customs home with them after spending some time in enemy territory. Since people from different cultures had fewer interactions with each other than they do today, it took years and decades for cultural ideas to spread.
Today, however, culture and traditions spread very quickly due to advanced technology such as the internet, which allows people from different cultures to interact freely. In today's melting-pot society, many people have varied cultural heritages. For example, it's possible for a modern family to have members of different religions, ethnic groups and nationalities. This creates a world where distinct cultural lines are blurred and new cultures are developed. Many children growing up in today's world follow extremely varied cultural customs.