There are diverse reasons why people like olive wood rosaries, crucifixes, or other religious objects. From my understanding the manufacture of these objects has been a source of income for Palestinian Christians for many generations. Also the wood used is pruned from ancient olive trees which possibly have been around for thousands of years. I have an olive wood rosary that I have carried for a long time. Also these items can make very nice gifts for holidays or special occasions. I also have a rosary made of olive pits, although I believe this one is from Rome and not the Holy Land.
Although not directly related to the rosaries or carvings, olive oil plays a significant part in our worship. It is used in various unctions, and burned in oil lampadas at home or in church.
Best wishes;
Stefan-Ivan