Inside repeater you have to take two div in one div put record fields using <apex:outputField> and in second div put record fields using <apex:inputField> by default set style="display:none" of DIV one and style="display:block" of DIV second. The important point is to take record  id in DIV id because it will be always different and you don't need to worry about dynamic id of the DIV. Onclick of the DIV call a javaScript function with recordId as parameter and you can use this id as Row Id. You can pass this recordId in controller to use.

Please find below is the sample code:

<apex:outputPanel id="updateDataPnl">

    <apex:repeat value="{!account}" var="a">

        <divhttp://a.id/" target="_blank">a.id}" ondblclick="HideShow('show',this,'{!a.id}')" style="display:block" width="30%">

           <a href="#"http://a.id/" target="_blank">a.id}')"><apex:outputField value="{!a.Name}"/></a>

                                </div>

        <divhttp://a.id/" target="_blank">a.id}" style="display:none" width="30%">

                                                <a href="#"http://a.id/" target="_blank">a.id}')"><apex:inputField value="{!a.Name}"/></a>

                                                <input class="btn" value="Save" onclick="UpdateRec('{!a.id}','{!a.Name}')"/>

                                                <input class="btn" value="Cancel" onclick="HideShow('Hide',this,'{!a.id}')"/>

        </div>

    </apex:repeat>

</apex:outputPanel>

<script>

    function HideShow(mode,rid,aid)

    {

        var rowid = rid.id;

        var strid1 = 'OutputLbl:' + aid;

        var strid2 = 'InputLbl:' + aid;

        if(mode == 'show' && rowid == strid1 )

        {

            document.getElementById(strid1).style.display='none';

            document.getElementById(strid2).style.display='block';

        }

        if(mode == 'Hide')

        {

            document.getElementById(strid1).style.display='block';

            document.getElementById(strid2).style.display='none';

        }

    }

</script>

<apex:actionFunction name="UpdateRec" action="{!UpdateEditedRec}" rerender="updateDataPnl" >

    <apex:param assignTo="{!propId}" value=""/>

    <apex:param assignTo="{!propName}" value=""/>

</apex:actionFunction>

</apex:form>

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