I'm sorry, I'm not entirely clear on what's going on with your yucca, so I'll try to answer in a "if/then" way. A yucca (the kind commonly used as a houseplant, sometimes called a soft yucca) consists of one or more main trunks (called canes,) with green things directly attached to it -- those are the leaves. Sometimes a smaller branch-like piece will emerge from the main cane, then it will have leaves coming off of it, and it's called a head.
The leaves do not root. If you put the leaves that you removed into water, they will just sit there for awhile looking quite green and lovely, but they will never make roots.
If you removed one or more heads from the cane, they will root. It's the woody part that roots, not the leaves. However, you don't want to keep them in water as they will likely rot. You want to put them into soil right away, which is what the articles mean when they talk about propagation. Keep the soil slightly moist until roots start to grow.
Another way to propagate, or root, the yucca, is to cut the main stem into pieces (any size will do, but 8-12" is good,) and put those pieces into soil. You can leave foliage on the top part, but remove leaves from the part that you stick into the dirt.
Most plants need to be in soil, not water. There are a few types of plants that can adapt their roots to living in water all the time, but most plants, while they survive awhile in water, will live much longer and more vigorously in soil. Also, if you have cuttings, mostly they should be rooted in soil, not water. Water roots and soil roots have certain differences, so the plant cutting rooted in water still has to grow new roots when it goes into the soil.
I hope this answers your questions. If not, don't be shy about writing in again.