Fit to size of UI element with child Text
If you have a UI element, such as a Button, that has a background image and a child Game Object with a Text component on it, you probably want the whole UI element to fit the size of the text - maybe with some padding.
In order to do this, first add a Horizontal Layout Group to the UI element, then add a Content Size Fitter too. Set the Horizontal Fit, the Vertical Fit, ot both to the Preferred setting. You can add and tweak padding using the padding property in the Horizontal Layout Group.
Why use a Horizontal Layout Group? Well, it could have been a Vertical Layout Group as well - as long as there is only a single child, they produce the same result.
How does it work?
The Horizontal (or Vertical) Layout Group functions both as a Layout Controller and as a Layout Element. First it listens to the layout information provided by the children in the group - in this case the child Text. Then it determines how large the group must be (at minimum, and preferrably) in order to be able to contain all the children, and it functions as a Layout Element that provides this information about its minimum and preferred size.
The Content Size Fitter listens to layout information provided by any Layout Element on the same Game Object - in this case provided by the Horizontal (or Vertical) Layout Group. Depending on its settings, it then controls the size of the Rect Transform based on this information.
Once the size of the Rect Transform has been set, the Horizontal (or Vertical) Layout Group makes sure to position and size its children according to the available space. See the page about the Horizontal Layout Group for more information about how it controls the positions and sizes of its children.