It depends on the express wording and scope of the easement and the person to whom the easement is granted. If it is a utility easement reserved for the power companies, your neighbors cannot park there and use it as their own. Moreover, unless it is a public easement, your neighbor has no right to park on your property.
DISCLAIMER: Brandy A. Peeples is licensed to practice law in the State of Maryland. This answer is being provided for informational purposes only and the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship. For legal advice relating to your specific situation, I strongly urge you to consult with an attorney in your area. NO COMMUNICATIONS WITH ME ARE TO BE CONSTRUED AS ARISING FROM AN ATTORNEY-CLIENT RELATIONSHIP AND NO ATTORNEY-CLIENT RELATIONSHIP WILL BE ESTABLISHED WITH ME UNLESS I HAVE EXPRESSLY AGREED TO UNDERTAKE YOUR REPRESENTATION, WHICH INCLUDES THE EXECUTION OF A WRITTEN AGREEMENT OF RETAINER.
An easement gives someone who doesn't own your property the right to use a portion of your property for a specific purpose. Your having a utiltiy easement on your property would not give your neighbor the right to park there. However, in many neighborhoods, the county right of way for roads and sidewalks is not fully used. Many times homeowners grow grass on this unused public right of way, thinking it is their property. Your neighbor would have the right to park on the public right of way. To make sure of exactly what your rights are, you should take a survey of your property and a copy of your title insurance policy to an experienced real estate lawyer in your area.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. Actual legal advice can only be provided after completing a comprehensive consultation in which all of the relevant facts are discussed and reviewed.
Is the grassy area between a sidewalk and the street (also called the "parkway")? if so, as Attorney Deason mentioned, while it is still your land for maintenance purposes, it belongs to the city or municipality as a utility easement for use in future road projects or other utility needs . If that is the case and unless there are existing ordinances that make parking in the parkway illegal, then your neighbor is correct and has every right to be there. Many cities, particularly those that plant grass and maintain the parkways prohibit it or only allow it on given days. Additionally, cars parked in the parkway cannot touch either the street or the sidewalk, or they will find themselves in violation of ADA rules.
Information provided here is anecdotal and should not be relied upon or considered legal advice. Every matter is different and answers given here are general in nature and may not reflect current Florida law at the time you are reading this posting. Please contact an attorney for legal advice concerning your matter.