One of the reasons that cocaine is so addictive is its highly reliable property of inducing powerful feelings of euphoria - typically at around 0.3-0.6 mg/kg of body-weight.

Since the 1990s, the reasons for this effect have been assumed to be because of its ability to block dopamine transporters (DATs) in the brain. The DATs function is to enable the 're-uptake' of dopamine in circulation ; when 'blocked' by the drug, dopamine levels build up - and these increased levels have been assumed to be the cause of the euphoric feelings..

In the past few decades however, many other substances have been discovered which block DATs far more efficiently - but do not induce any feelings of euphoria.

The long held view is cocaine's pharmacological effects are mediated by monoamine reuptake inhibition. However, drugs with rapid brain penetration like sibutramine, bupropion, mazindol and tesofensine, which are equal to or more potent than cocaine as dopamine reuptake inhibitors, produce no discernable subjective effects such as drug “highs” or euphoria in drug-experienced human volunteers. Moreover they are dysphoric and aversive when given at high doses. In vivo experiments in animals demonstrate that cocaine's monoaminergic pharmacology is profoundly different from that of other prescribed monoamine reuptake inhibitors, with the exception of methylphenidate. These findings led us to conclude that the highly unusual stimulant profile of cocaine and related compounds, eg methylphenidate, is not mediated by monoamine reuptake inhibition alone."

Source : Neuropharmacology Volume 87, Pages 19-40

Therefore, a complete explanation of the way(s) in which cocaine affects the brain to produce euphoric feelings is currently lacking.

Note: Some of the drug's other properties, such as its ability to block pain, are broadly understood.