Was ist rel = "pingback" und wozu dient dies auf meiner Website?

It's "Pingback"

What is Pingback?

Pingbacks (also known as trackbacks) are a form of automated comment for a page or post, created when another WordPress blog links to that page or post.
When you publish a new blog post, WordPress attempts to ‘ping‘ all the sites that were linked to in your post. i.e. Your WordPress website is informing other websites that you’ve linked to them.
When you receive pingpacks, then it means someone else has linked to one of your posts or pages. (:source^) (also learn more: WordPress.com Support, Wikipedia, and the Codex glossary)

And a more details about Pingback and Trackback, look here:

Codex: Pingbacks

Removing Pingback

To get rid of the pingback URL, just delete the line from your header.php:

<link rel="pingback" href="<?php bloginfo( 'pingback_url' ); ?>" />

The following article may help you understand, why:

Minimizing HTTP Requests with WordPress Themes - ClickNathan.com

Answers

Now come to your questions:

1. What is the use of this?

Answer: If you read all the resources, you now understand what's the use of it.

2. Does this link makes any problems?

Answer: No, it's just make a new query to the database, if the pingback URL is not defined directly. If defined programmatically then it just query the database once every page load and retrieve the pingback URL from db. It's not good for a healthy site to ping database for less important things. And if you read the links, pingback is not important.

But till we can seek:

• Trackbacks and Pingbacks: Positive (+)
• Trackbacks and Pingbacks: Negative (-)