Electricity is made up of both positive and negative charge. Negative charge flows from negative to positive and positive flows in the opposite direction. Typically, a storm cloud will have polarised charge with positive at the top and negative at the bottom. Hence the base of the cloud is more nagative than the 'ground'. When the charge builds up sufficiently this negative charge will discharge to ground in a series of 'strokes' in quick succession (lightning). However, this is equivalent electrically to a positive charge flow in the opposite direction. Hence, because of an out of date convention which states that current flows from positive to negative (positive charge flow) the 'conventional current' in the initial strokes flows from ground to the more negative cloud.
Still with me - well it gets more complicated. After the initial negative strokes discharge the base of the cloud its top is left positive. If the positive charge is sufficient this charge can cause an additional positive stroke and the 'conventional current' flows to ground!