We don't typically celebrate a saint's birthday in the church. We usually celebrate the day of his or her death. Most feast days are when we think the particular saint died or was martyred. Birthday celebrations are reserved for Jesus (Christmas) and Mary (September 8th).
And for Saint John the Baptist.
Yes, today, June 24th, the Church celebrates the “Solemnity of the Nativity of Saint John the Baptist.” Even though it falls on a Sunday this year, we still celebrate it. As if it were Christmas, the Baptist's Birthday trumps the 12th Sunday in Ordinary Time, which would have been this weekend.
We do indeed celebrate John's death (August 29th), but so important is John the Baptist that we also celebrate his birth. He is one of the few saints who receive multiple feast days: Joseph, Peter, Paul, and Mary.
John the Baptist's birth is six months after the birth of his cousin, Jesus Christ. Christ's birthday is around the winter solstice, when days begin to grow longer. The Baptist's birthday is around the summer solstice, when days begin to grow shorter. “He must increase, I must decrease” (Jn 3:30).