People in media often refer to much needed help as 'the cavalry' arriving. Why was cavalry so good as reinforcement to deserve this, and where has this saying come from?

I don't think there's a specific, singular reason for this, however, I can point to several instances where the cavalry did indeed save the day, and why.

Before the Napoleonic corps system, where all arms (infantry, cavalry and artillery) were integrated into one unit, armies still marched dispersed, but cavalry often separated from the infantry and artillery - for several reasons. The cavalry could move faster, forage, do recoinnasance and attempt to deny the enemy the same forage and recoinnasance. In many battles during this era, a skillful commander could move fast enough to Ccatch the enemy still separated - without his cavalry, an enemy would be at a serious disadvantage in any battle, as he would be unable to counter quick cavalry movements against his flanks or rear.

The Swedish army caught the Imperials without their cavalry at Lützen 1632 - while Pappenheim soon arrived with the Imperial cavalry, at the start of the battle, the Imperials were at serious disadvantage. Pappenheim died in the battle, and the letter, soaked with his blood, urging him to come to the aid of the Imperial army is still preserved.

At Grodno 1706, the Swedish army managed to separate not only the Russians from the Saxonians, but also separate the Russian army from their own cavalry through manouvre warfare - the Russian infantry and artillery was forced into Grodno and then forced to risk a daring breakout. More than 17 000 Russians died of starvation, disease and during the pursuit of the breakout. In that case, the cavalry never came to save the day.

Even when the cavalry was not absent, it could become absent during the battle. During the Battle of Lund 1676, the Swedish cavalry drove the Danish cavalry from the field and set off in a long pursuit to make sure the enemy did not reform. In the meantime, the superior Danish infantry and artillery was slowly and bloodily grinding its Swedish counterpart down. It was not until the majority of the Swedish cavalry and the King returned to the field that the Swedes won the battle.

However, the main source of this, at least in US media, could be from the conflict with the Native Americans in the west. These regions were garrisoned by federal cavalry (as infantry often was too slow to counter the horse-mounted Braves). In any case of an attack by Native Americans, it would be the cavalry that would respond and come to save any beleaguered settlers, cowboys or farmers.

Thus help from the authorities in grave situations would quite literally come in the form of the cavalry arriving.