Alkenes can react with electrophiles that are not strong acids such as borane (BH3 ). The reagents studied here are classified as 'neutral.' These conditions do not favor the formation of carbocation intermediates (they are strong acids!). The experimental evidence supports this fact as well - rearrangements are not observed in the reactions below and they are stereoselective.
In the hydroboration-oxidation, water is added across the alkene (H and OH). In the first step, a trialkylborane is formed. The second step oxidizes the trialkylborane to alcohols. The reaction is regioselective for the OH adding to the less substituted side ("anti-Markovnicov"). It is stereoselective - a syn addition of H and OH to the same face of the alkene.
The regiochemistry and stereochemistry are set in the hydroboration step of the reaction (a reduction!). We use a mechanism to explain the outcome. The oxidation occurs with retention of stereochemistry.