There are two types of tickling: 

1. Knismesis: triggered by a light movement across the skin. Think of a feather across the sole of your foot – that is knismesis. This type of ticklishness is experienced by many types of animals. Knismesis rarely produces laughter and is more akin to an itching sensation and can be irritating. Knismesis can be self-induced.
2. Gargalesis: this type of tickling is only found in certain mammals and is induced by applying pressure repeatedly to areas sensitive to tickling like under the arms, ribs or feet. Gargalesis often results in laughter even though it can be unpleasant or even painful. You cannot tickle yourself with the gargalesis form of tickling.

Possible Evolutionary Reason for Knismesis

The probable evolutionary reason for knismesis is that it prompts us to rub, scratch or slap at the tickled spot. This is useful as knismesis can be caused by an insect or parasite landing on, or walking across, skin.

Possible Evolutionary Reasons for Gargalesis

There are two primary theories why gargalesis type tickling evolved. They are not necessarily mutually exclusive.

One theory is that tickling helps form social bonds. As reported in Popular Science, Robert R. Provine, a neuroscientist at the University of Maryland, explains that tickling is partly a mechanism for social bonding between close companions and helps forge relationships between family members and friends. The smiling and laughter that occurs between tickler and ticklee may enhance relationships. Evidence of this is that parents tickle their children when they play and couples often tickle each other during courtship. Children often play tickle each other as their friendships develop.

Another theory relates to the development of combat skills:

Tickle evolved to promote protection of areas that would be most vulnerable during arm-to-arm combat. The idea is that ticklishness is such areas motivates one to protect these areas and thereby confers an adaptive advantage . . . . This provides a possible explanation for the pulling away and fending off movements frequently encountered during tickling. 

-C.R. Harris of University of California San Diego from this paper 

Infants don’t laugh until about 4 months of age and are not ticklish until about 6 months old. As adults, we tend to become less ticklish and many outgrow being ticklish by their 40s.