As symbols of the Christian faith, the Crown of thorns and the three nails of the crucifixion are emblematic of the passion- the suffering and death of Jesus. According to biblical accounts, the crown of thorns mocked Christ’s claim to the throne of David.
The nails, of course, refer to the nails of the crucifixion. Nails are sometimes worn by modern Christians as an alternative to the crucifix, although some evangelical Christians view the nail as a symbol of the Devil.
Curiously, the symbolism of the three nails arrayed as pictured above pre-exists Christianity; it is found occasionally on amulets to solar deities and may have once had a different meaning.