This example shows the "flip-flip" method where ANY graphic can be made into a repeating background graphic without visible seams.

If you Google "background textures" and choose the images tab, you will see a variety of textures. Some of these are subtle enough to function as a texture behind a block in a Web page, while others are far too busy. Some you find won't even tile (repeat) nicely because the seams are visible.

Consider a random graphic like this one: You can see all the seams when you tile it as shown below.
To tile properly, an image needs "symmetry around the edges" so to speak. It should become clear what that means after you see the solution how to create such symmetry.

First, copy the graphic, flip it horizontally (mirror around a vertical axis), and paste the flipped copy directly beside the original:
Second, copy all of that and flip it vertically (mirror around horizontal axis): Now when tiled as below, all of the edges match up and it appears seamless.
Be sure to see the comments further below.
Although it looks kind of cool, this would probably not be a good image to use as a textured background in most situations.
If you edit it to put an opaque layer on top to tone it way down, it does get substantially more subtle but still may be too "busy" to put text on top of, for example.
When you get creative with this technique, you can make some pretty cool repeating textures.

The "flip-flip" method shown in this example is fairly easy and intuitive. But its also interesting what you find when you search for other ways to accomplish this. For example this one shows a technique to "smooth the seams" and this one just seems overly complicated given how easy the flip-flip is technique.