This page will hide and show the output panel when a button is clicked.

Apex Class for Rerender the output panel

public class RenderExampleClass {
    /****get set varaible which will carry the true or false condition to the page****/
    public Boolean showPanelHistory{ get; set;}
    /****get set varaible which carry the list of accounts to the page****/
    public Account accountList{ get; set;}
    
    /****Acction method which is used in the page which acts like switch*****/
    public PageReference showpanel(){
       if(showPanelHistory == false) {
            showPanelHistory = true;
        }
        else if(showPanelHistory == true){
            showPanelHistory = false;
        }
        return null; 
    }
    /***Example methos that to query the list of accounts***/
    public void accountList(){
        accountList = [
            SELECT  Id,
                    Name,
                    Type
            FROM    Account
            ];
    }
    /***** Setting up showPanelHistory = false directly in constructor 
    so when page loads the switch willl be in false condition********/ 
    public RenderExampleClass() {
        showPanelHistory = false;
    }
}

Visual force page for Rerender output panel

<apex:page controller="RenderExampleClass">
    <apex:form >
        <apex:commandButton value="Show Section" action="{!showpanel}" rerender="showpanel">
        </apex:commandButton>
        <apex:outputPanel id="showpanel">
            <apex:outputPanel rendered="{!showPanelHistory}">
                <apex:pageBlock title="List of Accounts"> 
                    <apex:pageBlockSection >
                        <apex:outputField value="{!accountList.Name}"/>
                        <apex:outputField value="{!accountList.Type}"/>
                    </apex:pageBlockSection>
                </apex:pageBlock>    
            </apex:outputPanel>
        </apex:outputPanel>
    </apex:form>    
</apex:page>