The monsters visually appear to be ghostly beings, while the Trap Monsters appear to be animated armor/weapons surrounded by ghostly flames. They use the naming scheme "The Phantom Knights of {adjective} {clothing item/weapon}" in the TCG, or "Phantom Knights {adjective} {clothing item/weapon}" in the OCG, with the namesake item being featured in the artwork of each respective card.
Etymology
The adjectives for the monsters appear to be words related to disrepair, disuse, and emptiness; while the adjectives for the Trap Monsters seem to relate to darkness, death, emptiness, and mistake.
In Japanese, their Kanji reads "幻影騎士団" (Gen'ei Kishidan)
"The Phantom Knights" monsters involve manipulating their cards while they are in the Graveyard. Though they have other effects, the Main Deck monsters share a common effect of banishing themselves from the Graveyard in order to search each other/their Spell/Trap Cards out or place each other/their Spell/Trap Cards in the Graveyard. Their Spell and Trap Cards also have effects that can be activated from the Graveyard in order to Special Summon more "The Phantom Knights", including multiple Trap Monsters. These plays are meant to set up the Xyz Summon of Rank 2-4 DARKXyz Monsters, supporting them with stat-increasing and protection effects.
As the deck is heavily reliant on monster effects on the field, cards that negate monster effects such as "Skill Drain" and "Mystic Mine" will heavily limit the deck's abilities.