I have one table as blog_posts

+---------+-----------+
| postID | categoryID |
+========+============+
| 1      |  1         | 
+--------+------------+
| 2      |  1         |
+--------+------------+
| 3      |  2         | 
+--------+------------+  
| 4      |  4         | 
+--------+------------+

and another is blog_category

+---------+-----------+
| CategoryID | catName |
+========+============+
| 1      |  cricket   | 
+--------+------------+
| 2      |  sports    |
+--------+------------+
| 3      |  football  | 
+--------+------------+  
| 4      |  tennis    | 
+--------+------------+

now i want to display the categories and how many post are there on category as well. like categoryID 1 is there in postID 1 and 2 so, it will show cricket , posts 2. right now i am only fetching the categories only which is easy :P

     <ul>
       <?php
       if (mysqli_connect_errno()) {
      echo "Failed to connect to MySQL: " . mysqli_connect_error();
    }
    $result = mysqli_query($conn,"SELECT * FROM blog_category ");
    while($row = mysqli_fetch_array($result)) {



    ?>
     <li>
            <a class="f-categories-filter_name" href="blog-cat.php?id=<?php echo $row['categoryID'];?>"><i class="fa fa-plus"></i><?php echo $row['categoryName'];?></a>
<span class="b-categories-filter_count f-categories-filter_count">**I want to display here number of posts of that category**</span>
        </li>
        <?php } ?>
    </ul>

To get the number of posts in each category you need to use the following SQL query:

SELECT 
   blog_category.*, 
   COUNT(blog_posts.postID) AS cnt
FROM 
   blog_category
INNER JOIN
   blog_posts
ON
   blog_posts.categoryID=blog_category.categoryID
GROUP BY
   blog_category.categoryID;

So it will be something like this:

 <ul>
 <?php
   if (mysqli_connect_errno()) {
       echo "Failed to connect to MySQL: " . mysqli_connect_error();
   }
   //here we use a modified query
   $result = mysqli_query($conn, "SELECT 
   blog_category.*, 
   COUNT(blog_posts.postID) AS cnt
FROM 
   blog_category
INNER JOIN
   blog_posts
ON
   blog_posts.categoryID=blog_category.categoryID
GROUP BY
   blog_category.categoryID;");
       while($row = mysqli_fetch_array($result)) {
    ?>
     <li>
            <a class="f-categories-filter_name" href="blog-cat.php?id=<?php echo $row['categoryID'];?>"><i class="fa fa-plus"></i><?php echo $row['categoryName'];?></a>
<span class="b-categories-filter_count f-categories-filter_count"><?php echo $row['cnt'];?></span>
        </li>
        <?php } ?>
    </ul>

Yuo can obtain the data direcly with a query

the full list

select blog_category.catName   group_concat(blog_posts.postID)
from blog_posts
inner join blog_category on blog_category.CategoryID = blog_posts.CategoryID 
group by blog_category.catName ;

or a singole category

select blog_category.catName   group_concat(blog_posts.postID)
from blog_posts
inner join blog_category on blog_category.CategoryID = blog_posts.CategoryID 
where blog_category.CategoryID = 1
group by blog_category.catName ;

You have to change your SQL query to fetch data. There are many way to join it. I've write one.

SQL

SELECT blog_category.* , count(*) as total_post 
FROM blog_category INNER JOIN blog_posts 
ON blog_category.CategoryID = blog_posts.categoryID 
GROUP BY blog_category.Category

Full Code

<ul><?php

  if (mysqli_connect_errno()) {
    echo "Failed to connect to MySQL: " . mysqli_connect_error();
  }

  $result = mysqli_query($conn,"SELECT * FROM blog_category ");

  while($row = mysqli_fetch_array($result)) {

    ?><li>
      <a class="f-categories-filter_name" href="blog-cat.php?id=<?php echo $row['categoryID'];?>"><i class="fa fa-plus"></i><?php echo $row['categoryName'];?></a>
      <span class="b-categories-filter_count f-categories-filter_count"><?php echo $row['total_post']; ?></span>
    </li><?php

  }

?></ul>

For more information

SQL join : http://www.w3schools.com/sql/sql_join_inner.asp
SQL Count : http://www.w3schools.com/sql/sql_func_count.asp