This is the 14823rd most frequent Russian word.
побеждены
"Defeated."
Here 'побеждены' metaphorically describes the negation or overcoming of hopes by reality.
Их надежды оказались побеждены суровой реальностью.
Their hopes were defeated by the harsh reality.
In this sentence, 'побеждены' describes the military context where the enemy army has been defeated.
Армия врага была полностью побеждена.
The enemy army was completely defeated.
The word 'побеждены' is used in the past tense passive voice to indicate that the subject (we) experienced defeat.