Annie,
As Bonnie said, this will depend on what is in your Associations governing documents.
One thing to remember is that Directors and Officers are two different positions. Directors are elected by the membership or appointed by the Board (typically to fill vacancies). Officers are usually appointed by the Board. If the Board appointed someone into that position, the Board may remove them from that position.
Typically, the membership elects the Directors and the Board appoints the Officers. When this happens the Board is allowed to remove you from Office but not from being Director unless the governing documents provide that additional authority. Typically, when this authority is provided it is a conditional authority (example: Director does not attend 3 meetings).
It's typical for Associations to be incorporated as a not-for-profit corporation. When this happens, in addition to HOA/COA laws, the corporation must comply with the applicable corporate law. Since corporate laws typically address procedures, it's a good idea to review them when procedures are being questioned:
Per
FL 617.0842 Resignation and removal of officers this statute allows Officers of the Association to be removed from Office by the Board.
Per
FL 617.0808 Removal of directors Any member of the board of directors may be removed from office with or without cause by:
1. Except as provided in paragraph (i), a majority of all votes of the directors, if the director was elected or appointed by the directors; or
2. A majority of all votes of the members, if the director was elected or appointed by the members.
Hope this helps,
Tim