How did tattoos became popular part of todays culture? (how did they became so mainstream in the society)
Tattoos have been around for a long time. I am not sure exactly, but they're been around about as long as people have been! They are becoming more acceptable in our society, and more mainstream. It is because more people know someone who has one, and they are not considered part of a criminal element.
Tattoos used to be looked down upon not too long ago. Now people from all walks of life, all ages, various personalities, and in all types of professions have them (even if they keep them covered up at times). I believe that one reason they have become accepted by mainstream society is because of their prevalence among celebrities. Another reason for their acceptance is that people are now more comfortable with self-expression and individualism.
Cultures around the world have a history of tattooing that goes back hundreds of years. In the United States, I think the trend probably goes farther back than the entertainment industry. Sailors and prisoners have practiced the art long before the rappers. One reason they might be popular in the United States is that it gives people autonomy over their own bodies and looks.
It is not always possible to identify exactly how something becomes a part of culture. I would argue that, in the United States at least, tattoos have become more popular in part through athletes and musicians. I think that tatoos first became common on musicians like rap artists. Then athletes started having them and now they have become much more common.