This is the 14586th most frequent Russian word.
первомайские
"Первомайские" refers to something related to May Day (International Workers' Day) or May-related celebrations.
Here, 'первомайские' is an adjective derived from 'Первомай' (May Day) and is used to describe the holidays associated with May 1st.
Первомайские праздники всегда приносят радость.
The May Day holidays always bring joy.
'Первомайской' here modifies 'демонстрации' (demonstration), indicating that this demonstration is related to May Day celebrations.
Во время первомайской демонстрации люди выходят на улицы с транспарантами.
During the May Day demonstration, people take to the streets with banners.
In this context, 'первомайские' describes 'цветы' (flowers), potentially referring to flowers traditionally blooming or associated with May 1st.