checkbox click event in repeater control

For determining whether the Checkboxes are checked, you need to look for the control first by using FindControl[^] method of the repeater item.

Suppose this is your repeater and Button2 is your export to PDF button:

<asp:Button ID="Button2" runat="server" onclick="Button2_Click" /><br />
    <asp:Repeater ID="Repeater1" runat="server" OnItemCommand="Repeater1_ItemCommand">
    <ItemTemplate>
            <asp:CheckBox ID="Checkbox1" runat="server" />
            <asp:Label ID="Label2" runat="server" Text='<%#DataBinder.Eval(Container.DataItem, "Name")%>' />
            <br />
    </ItemTemplate>
    </asp:Repeater>

You can accomplish your goal by implementing something similar to the one below.

protected void Button2_Click(object sender, EventArgs e)
{
    foreach (RepeaterItem item in Repeater1.Items)
    {
        if (((CheckBox)item.FindControl("Checkbox1")).Checked)
        {
            //Do something
        }
    }
}

Now that can filter checked items, you can use some third party API like ITextSharp[^] to export data to PDF. Here[^] is a good tutorial for starters about the API.