What is the significance of El Dia de los Reyes and when is it?

El Dia de los Reyes corresponds to Twelfth Night/Epiphany, i.e. 6th of January.

It means The Day of the Kings, because traditionally in Spain and Latin America, The Three Kings'/Wise Men's adoration of Jesus is celebrated on that day, sometimes with formal celebrations, but also e.g. the giving of sweets or presents to children (a la Santa Claus, but publicly rather than domestically, and on 6 January, not 24/25 December)) by three men in gorgeous robes representing the Three Kings.