Question
Several white round spots on the base of branches.  When I picked a few off the branch, they had a small round bloody-like center. What is that?  Also, one of the branches broke off like dry wood. I don't know what kind of organism it is and can it be spread to humans?

Answer
Hi Rose,

I suspect that your holly plant has an insect problem.  Based on the description, my guess is that this is a scale insect.  Below are two links to publications with lots of pictures of insects of holly including scales.  Look at these links and see if you can determine exactly which you have.  Without an image, I cannot say for certain so you will have to do a close inspection of the plants.
http://edis.ifas.ufl.edu/pdffiles/IN/IN64900.pdf
http://www.ces.ncsu.edu/depts/ent/notes/O&T/specificplants/note143/note143.html

If you do confirm that this is a scale problem, there is a great deal of info at the following link about scales including life cycle and control options.  Take a look at the fact sheet an let me know if you have additional questions.
http://www.ipm.ucdavis.edu/PMG/PESTNOTES/pn7408.html

Good luck,
--Jen