Can I set and show “important” post in my blog?

Yes of course. One of the ways to achieve this is by adding an extra category to your posts which you call ‘sticky’ or ‘important’ or something like that.

For the example I will choose ‘important’. To only get the important posts you can write a loop which loops through this category.

For example:

<?php 
$args = array( //arguments for the loop
    'post_type' => 'post',
    'category' => 'important',
    'posts_per_page' => 1, //show one post from the important posts
    'order' => 'DESC' //order descending, show the lastest posts first
);

$query = new WP_Query( $args );
if ( $query->have_posts() ) : while ( $query->have_posts() ) : $query->the_post();
?>

HTML HERE, FOR EXAMPLE:

<div class="news important">
   <?php the_post_thumbnail(); ?>
   <h2><?php the title(); ?></h2>
   <?php the_excerpt(); ?>
</div>
(ofcourse you can also write this within the php, do what you prever)

And then close the loop

<?php endwhile; endif; ?>

I didn’t test this, but I hope it can point you in the right direction to solve this.
For more info: WP_Query

You can also go for a sticky posts plugin, but writing yourself gives you more flexibility.