Data manipulation is where you take your data and change it to try and make it easier to read, or to make it more organized. For example, you could organize a log of data in alphabetical order, which would make the entries a lot easier to read. Data manipulation is typically used for web server logs so that there are more website owners that can view the most popular pages and traffic sources.
People in accounting fields or other jobs that tend to work a lot with numbers will often manipulate data so that they can figure out their costs of products, how well the merchandise is selling each month or week, potential tax obligations, or trends in sales. Stock market analysts will typically use data manipulation so that they can predict trends within the stock market, and how their stocks could end up performing in the future.
Computers are also able to use data manipulation to display information to the users in a way that is more meaningful, based on the software programs code, data formatting, or web page that is defined by the user.