Kissing between sexual and/or romantic partners occurs in over 90 percent of human cultures (Eibl-Eibesfeldt, 1970; Fisher, 1992). Even in cultures where kissing is nonexistent or condemned, sex partners may blow in each other’s faces, lick, suck, or rub their partner’s face prior to intercourse (Ford and Beach, 1951).

Some non-human animals appear to engage in kissing-like behaviors, as well (Geer, Heiman, and Leitenberg, 1984). For instance, de Waal (2000) claims that bonobos regularly engage in bouts of deep tongue kissing.

Although kissing is a widespread practice among humans, few investigators have attempted to assess the adaptive significance of kissing behavior.

Source : Sex Differences in Romantic Kissing Among College Students: An Evolutionary Perspective Evolutionary Psychology, 5(3): 612-631

There are various plausible explanations as to how and why it could have originated. - e.g. food swapping, immunity balancing, the mammalian suckle reflex, mate suitability evaluating (chemical cues) etc. But no one theory covers all its manifestations*, and none has been accepted by evolutionary scientists as a general overall explanation.

Given that kissing is a fairly obvious disease vector, it presumably must have (or have had) strong evolutionary advantages. See The ancient history of kissing: Science, Vol. 380, No. 6646

*Wikipedia lists no less than eight different varieties.

Note: Some fish also 'kiss', see :Kissing Gouramis