This is the 424th most frequent Ukrainian word.
їх
"Their" or "them."
'їх' functions as a possessive pronoun, indicating ownership of the 'flowers'.
Це були їх квіти, залишені біля будинку.
These were their flowers, left near the house.
'їх' functions as a possessive pronoun modifying 'inspiration', signifying possession of the concept of 'inspiration'.
Джерело їх натхнення залишається невідомим.
The source of their inspiration remains unknown.
'їх' functions as a personal pronoun referring to 'them', the object of the action 'saw'.