It allows creatures that commonly feature lower than usual power to destroy any creature that they battle with.
As it does not choose creatures, it can be used to get around Unchoosable creatures such as Supernova Apollonus Dragerion. The creature with Slayer does not need to lose the battle in order to use it's ability due to its text change from DM-10, but usually creatures with slayer are low in power so they are easily destroyed. As a result, it can be used to exploit creatures with the Win All Battles ability and abilities such as ones from Amnis, Holy Elemental in order to destroy them.
This original wording of this ability was only featured on 4 English cards, 2 each in DM-01 and DM-03.
Since a Slayer's purpose is to lose a battle, it is generally seen in creatures with 4000 power or less. However, some newer creatures with slayer have high power, (Such as Truename Screaming Psycho) and they can be used to destroy a creature multiple times, such as linked Gods, Psychic Creatures with Release or Super Psychic Creatures.
Slayers also stack, so if a creature with multiple slayer abilities battles another creature, that creature is destroyed that many times.
The latest reminder text for Slayer reads;
Slayer(Whenever this creature battles, destroy the other creature after the battle.)
It originally read as
Slayer(When this creature loses a battle, destroy the other creature.)