Reach refers to a player's ability to deliver direct damage to the enemy hero, regardless of the state of the board. This generally refers to damage from spells and Hero Powers, but could include activated abilities.
Reach is strategically significant in achieving lethal when the opponent has control of the board, or the player simply has no board presence. Taunts can prevent the player from reaching the enemy hero with minions, and might even counter random target damage like that of Boom Bot, but cannot prevent direct targeted damage.
Sometimes, reach is achieved with a minion with charge, although they might not be as consistent against taunts, they still serve the purpose most of the time, expecially in minion-heavy decks. In addition, decks running such cards are generally able to build up strong board control.
Decks with a lot of reach have a strong ability to close matches once the opponent has reached a sufficiently low Health total. Reach goes hand in hand with burst, causing unstoppable damage from the hand. Decks with a lot of reach therefore tend to be especially dangerous at lower Health, making it wise to play cautiously against them. Underestimating a deck's reach can lead to abrupt defeat, with the opponent producing card after card of direct damage for a staggering one turn kill. Reach is frequently associated with aggro decks.
Reach metaphorically describes a deck's ability to reach a long distance to deal a decisive blow to the opponent; they may seem a long way from victory, but having enough reach can allow them to span the distance and secure the game. The term's use in Hearthstone can be compared to the ability to make a long shot in a sport like basketball: even if the opposing team's defenders keep the player a long way from their end of the court, with enough reach they can successfully make the shot and score for their team, winning the game in the nick of time.