Those guys are costaleros. Costaleros are those who carry the "pasos" in the processions The "pasos" are large and heavy floats with the life-size statues of the Christ, the Virgin Mary and other biblical characters.

Costaleros go under the paso and carry its weight on the back of their neck, which is why they wear that particular headdress (called "costal"). Each Costalero carries between 50 Kg and 70 Kg (about 100 lb) and they frequently switch teams. Each paso (float) weights 1 Ton or more, so they need about 20 to 40 Costaleros to carry it.

For more information about the Costaleros, read: es.wikipedia.org/wiki/Costalero and es.wikipedia.org/wiki/Costal

Traditional processions during the Semana Santa (Holy Week) in Sevilla, Spain