It was a crown used on certain occasions, though was never used during liturgical ceremonies.
The tiara was not always part of the papacy and initially was rather simple, as the Catholic Encyclopedia explains:
[T]he papal ornament for the head was, as is clear from the "Constitutum Constantini" and from the ninth Ordo of Mabillon (ninth century), merely a helmet-like cap of white material. There may have been a trimming around the lower rim of the cap, but this had still in no way the character of a royal circlet.
By the 13th and 14th centuries the tiara was embellished by the popes and became an ornate crown, reflecting the pope's temporal authority over all the kings and queens of Europe.
The last pope to wear the tiara was St. Paul VI, but he renounced its use on November 13, 1964, and donated it to the poor.
Refusal to wear the tiara
Blessed John Paul I was the first pope to refuse its use and St. John Paul II followed in line. He explained his reasoning during the homily of his inauguration Mass:
In past centuries, when the Successor of Peter took possession of his See, the triregnum or tiara was placed on his head. The last Pope to be crowned was Paul VI in 1963, but after the solemn coronation ceremony he never used the tiara again and left his Successors free to decide in this regard.
Pope John Paul I, whose memory is so vivid in our hearts, did not wish to have the tiara; nor does his Successor wish it today. This is not the time to return to a ceremony and an object considered, wrongly, to be a symbol of the temporal power of the Popes.
St. John Paul II wanted to place the focus on Jesus Christ and not the "power" of the pope:
Our time calls us, urges us, obliges us to gaze on the Lord and immerse ourselves in humble and devout meditation on the mystery of the supreme power of Christ himself.
He saw the tiara as an obstacle in the modern world to the proclamation of the Gospel. If he were to accept it and wear it, he felt that it would distract people from the central truths of the faith.
Every pope since then has refused the papal tiara and has not revived its use.
While it was seen as an important part of the papacy for many centuries, it is not essential.
St. Peter was certainly able to rule the Church without a tiara, and modern popes are able to rule in a similar way, placing the emphasis on Jesus Christ and the Gospel message.