Attributes (Japanese: 属性 Zokusei; Chinese: 屬性 Shǔxìng) are essentially the "Elemental" groups for each Monster Card. There are different cards made to support each "element", and there are popular monsters of each kind. It is possible for a monster to be considered part of multiple attributes via a card effect.
Real Monster Attributes
FIRE
See the main article, FIRE.
WATER
See the main article, WATER.
WIND
See the main article, WIND.
EARTH
See the main article, EARTH.
DARK
See the main article, DARK.
LIGHT
See the main article, LIGHT.
DIVINE
See the main article, DIVINE.
LAUGH
See the main article, LAUGH.
Monster Attributes taken from YCM wiki
TIME
See the main article, TIME.
Made-up Monster Attributes
KING
KING is an Attribute first seen on "Number 1958: The King of Pop" and "Number 1935: The King of Rock and Roll". According to NovaTsukimori, that Attribute can be found in the stone tablet form of "Shooting Star Dragon" which, instead of having the WIND Attribute, it has the kanji of king. So far, they can be supported by Precious Knight's effect when battling a Diamond Rare monster, while all KING-Attribute monsters (save for Shooting Star Dragon, who had that Attribute in its tablet form, but changed to WIND) are treated as LIGHT monsters.
MONEY
MONEY is a custom Attribute reflecting the element of money, and anything that has relationship with money and gambling. It appears that many of these cards are related to the "Tax Collector" archetype, spearheaded by "Number 200: Demonic Tax Collector - Zacchaeus", and take advantage of their destruction-evading effects to overwhelm their opponent. Their Xyz Materials are gray, and gray is the color associated with them. They first appeared in LHK's set, Infernal Flames of Destiny.
LOVE
LOVE is a custom Attribute reflecting the element of love and passion. It was made by LHK, in St. Valentine's Day. From the few information we have in hand, this Attribute's main strategy is to take control of cards, much like what lovers "take control of their love's hearts".