In a match situation, handicap match betting gives one team or player a virtual deficit to overcome (a handicap) at the start of the event - the opponent receives a virtual start. You bet on who will win with the handicap taken into account.
A +1.5 handicap means that 1.5 goals or points will be added to the full-time score for that game. For example, if the game finishes 2-1 and your team has only scored 1 goal, then 1.5 will be added to create an adjusted final score of 2-2.5, meaning the bet now wins.