The reason you have an item, such as a rosary or crucifix, blessed is twofold - 1 - the item is therefore dedicated to divine worship or veneration (ie the rosary is used to meditate on the life of Jesus and not as a piece of jewelry or decoration) and 2 - the Church has attached a plenary or a partial indulgence to the praying of certain prayers using the blessed item while meeting certain other conditions such as sacramental Confession and Communion.
ADORATION OF THE CROSS. A PLENARY INDULGENCE to those who in solemn liturgical action of Good Friday devoutly assist in at the adoration of the Cross and kiss it. (link also contains more information on indulgences and practices which are enriched with indulgences)
catholic.org/prayers/indulgw.php
In particular, there are indulgences attached to using a blessed rosary:
A partial indulgence may be gained once a day by the faithful who kissing a blessed Rosary, which they carry with them, at the same time recite the first part of the Hail Mary up to “Jesus” inclusive. There are others attached to the rosary but I didn’t quote them all in the interest of brevity.
theholyrosary.org/power.html
Also, it is necessary to dispose of blessed items, such as a broken rosary, in the approved manner.
Once a religious object is blessed and dedicated for divine worship or veneration, it must be treated with reverence and not be used in either an improper or profane way (cf. Code of Canon Law, no. 1171).
However, blessed religious objects break or wear from use. The basic rule for the disposition of these items is to burn or to bury them.
cukierski.net/disposingofblessedobjects.shtml (this link has more information on blessed objects and their uses)