An alternative lifestyle is one that is different than the norm. One example is vegetarianism. People who eat no meat are a minority. People who live in communes live away from everyday society. They do not participate in all that society has to offer. Some people practice alternative medicine. Once again this is different from the majority, making it an alternative lifestyle. Another alternative lifestyle is polygamy. Most people in the US only marry one person at a time. In polygamy, men are allowed to marry more than one wife, while women can only marry one man.
Another "alternative lifestyle" of today that breaks a previous social norm is non-traditional families. Once, the "nuclear family" was considered normal: a working father, stay-at-home mother and two kids.
Consider the television progression. Are you young enough to remember The Dick Van Dyke Show or Leave it to Beaver? Even The Simpsons and Family Guy portray this traditional family (although Family Guy adds a talking dog and grown up baby, so that might be a bad example).
Now families come in sorts of socially acceptable varieties. Two moms, two dads, unmarried men and women living together, mixed races, adopted children. Shows like Brothers and Sisters, Two and a Half Men, or Will and Grace portray non-traditional structures of what could be argued as more than just roommates, but families.
An alternative lifestyle is a lifestyle that is considered to be outside the norm for that particular culture. Some examples of alternative lifestyles may be gay, lesbian, transgender, transexual, bisexual, etc. An alternative lifestyle is not always focused on sexual orientation though. Some other example of alternative lifestyles are swingers, hippies, goth, and punk. These are all subcultures within a larger culture.
Alternative lifestyles are becoming more accepted into our society but people who live these lifestyles are still very often targets of prejudice and discrimination. These lifestyles have always existed but they are becoming more out in the open so the general public is more educated.