Tangible is able to be touched or having physical existence as opposed to intangible that is not actually a physical item. For example, a stock or bond is an intangible (even though there may be a piece of paper) whereas furniture or equipment is tangible.
Personal property is that which is not real property. Real property is land and the items attached to the land such as buildings.
So personal property is all of the stuff like furniture, equipment and such.
Each year the value of the personal property used in business or rental is reported (what was in service January 1 is reported by April 1) to the property appraiser of the county and a small percentage of the value is paid as tax.
"Property owners who lease, lend or rent property must also file."
The form and instructions are at http://dor.myflorida.com/dor/property/forms/current/dr405a.pdf
For more details see http://www.coj.net/departments/property-appraiser/tangible-personal-property-faq.aspx
"On Jan. 29, 2008, voters approved Amendment One - a property tax reform package that includes a $25,000 exemption for Tangible Personal Property. Businesses must file a tangible personal property return to qualify for the exemption. Businesses with assets under $25,000 must file an initial return, and will not be required to file again until their assets exceed the $25,000 threshold."
For most home rentals in Florida only one return will need to be filed in order to qualify for the exemption not to file because the total value of tangible personal property is less than $25,000.
Please ask if you need clarification.