I don't believe there's a way to provide a description to a local block.

However, you should be able to update the header in the language file as shown below.  

<?xml version="1.0" encoding="utf-8"?>
<languages>
  <language name="English" id="en">
    <contenttypes>
      <icontentdata>
        <properties>
          <newslist>
            <caption>New Header</caption>
          </newslist>
    </contenttypes>
  </language>
</languages>


 [Display(
            GroupName = SystemTabNames.Content,
            Order = 305)]
        public virtual PageListBlock NewsList { get; set; }

The second option is to update the group name attribute so it shows up on a separate tab where you can provide a more meaningful tab name.

There's also this: https://gregwiechec.com/2018/04/grouping-properties-using-header/

I know it's not exactly what you asked for, but I've written a blog post about how to display a help text (heading + description) wherever you want in edit mode. It could be at the very top of a tab, or in between propertyes. It could serve the same purpose, and maybe you can make use of something similar.

http://gulla.net/episerver-help-texts-improved/

Thanks Aniket and Tomas for replying to my query.

Tomas, your approach may help if I move the block to the top (as the first item) in the tab. The primamry objective is to provide some overal instruction while filling in the Block.

The help text in my approach can by placed anywhere. It does not have to be at the top of the tab like in my screenshot.