Arrows are extremely useful against large swarms of low health troops such as Minion Horde. They cost 1 more Elixir than the Zap, but they have a larger area of effect, and also deal more damage, being able to kill Minions up to two levels higher than themselves.
The spell can be used to finish off buildings that are extremely low on hitpoints.
It is possible to go for a push using a Giant and a Prince or any viable combination, knowing that the opponent will use low-hitpoint units such as Spear Goblins, Archers, and Minions. When the opponent tries to defend the Arena Tower, cast Arrows on the enemy units and secure a push.
Keep in mind that Arrows has a somewhat long travel time and will take a bit of time to reach their target. However, it is possible to "pre-cast" Arrows by placing them on a spot where the opponent is likely to drop a swarm of troops (e.g. on a Giant when the opponent has a Minion Horde). This move is extremely risky and can result in a waste of Elixir, but if used well it can also be quite worthwhile.
Arrows are a neutral counter to Goblin Barrel. When the opponent throws the Goblin Barrel, fire Arrows immediately once the Goblins spawn, and the Goblins will be destroyed. Arrows has a long cast time, so firing the Arrows slightly before the Goblin Barrel's impact will make sure that no damage is dealt to the Crown Tower.
You can bait the opponent to use their Arrows using low hitpoint troops. Then, use troops which the opponent cannot counter easily without Arrows like the Goblin Barrel and Minion Horde. However, keep in mind that the opponent may also have other area damage spells or troops, such as the Zap, Fireball, and Wizard.
Arrows are a great counter card towards decks that have a majority of low hitpoint units, such as the Skeleton Army.
The Log can be an alternative to it, as they have similar areas of effect and damage. The Log costs 1 less Elixir, pushes units back, and has a linear attack, but it can't damage air troops.