The concept is very well explained by the accepted answer, but I find that the more example one sees, the better it sinks in. Here's an incremental example:

1. Boss says "get me number of items we have in stock grouped by brand"

You say: "no problem"

SELECT 
      BRAND
      ,COUNT(ITEM_ID) 
FROM 
      ITEMS
GROUP BY 
      BRAND;

Result:

+--------------+---------------+
|  Brand       |   Count       | 
+--------------+---------------+
| H&M          |     50        |
+--------------+---------------+
| Hugo Boss    |     100       |
+--------------+---------------+
| No brand     |     22        |
+--------------+---------------+

2. The boss says "Now get me a list of all items, with their brand AND number of items that the respective brand has"

You may try:

 SELECT 
      ITEM_NR
      ,BRAND
      ,COUNT(ITEM_ID) 
 FROM 
      ITEMS
 GROUP BY 
      BRAND;

But you get:

ORA-00979: not a GROUP BY expression 

This is where the OVER (PARTITION BY BRAND) comes in:

 SELECT 
      ITEM_NR
      ,BRAND
      ,COUNT(ITEM_ID) OVER (PARTITION BY BRAND) 
 FROM 
      ITEMS;

Which means:

• COUNT(ITEM_ID) - get the number of items
• OVER - Over the set of rows
• (PARTITION BY BRAND) - that have the same brand

And the result is:

+--------------+---------------+----------+
|  Items       |  Brand        | Count()  |
+--------------+---------------+----------+
|  Item 1      |  Hugo Boss    |   100    | 
+--------------+---------------+----------+
|  Item 2      |  Hugo Boss    |   100    | 
+--------------+---------------+----------+
|  Item 3      |  No brand     |   22     | 
+--------------+---------------+----------+
|  Item 4      |  No brand     |   22     | 
+--------------+---------------+----------+
|  Item 5      |  H&M          |   50     | 
+--------------+---------------+----------+

etc...