Copy fitting can be enabled on a text frame containing variables.

It scales text content down to fit all text in the frame or scales the text content up to fill up empty space in the text frame.
The more text is added, the smaller the size and, vice versa, less text means larger size.

To enable copyfitting go to Variable Data tab > Variable Tools panel and click "Apply Copyfitting".
Copy fitting parameters can be defined via Copy fitting Styles (Styles tab) or a custom setting can be defined on frame level.

Style: select a copy fitting style or define custom settings
Between x and x % : sets lower and upper font size limits after copyfitting is applied.
Current: shows the applied percentage
Max. Lines : sets maximum amount of lines after copyfitting is applied
Only when there is overflow: copy fitting will only be applied if there 's to much text to display in the text frame
Affected frames behave as group: This applies only to frames using the same Copy Fitting Style.
When this is selected the copy fitting percentages for all frames individually will be compared and the value of the frame that has been copy fitted most is used to apply copy fitting to the other frames as well. See the image below for an example
Enable Leading
Enable Tracking

Example: Copy fitting across multiple non-linked frames

How does this work?

Having 3 paramaters to copyfit, might not give your intedted result. Therefore we want to explain what happens in the brains of CopyFitting.

Template designers can set minimal allowed tracking and leading in copy-fitting settings.

The maximum values for leading and tracking are defined by the text itself.

In other words, copy-fitting works in the following order:

Compact text (reduce leading/tracking)
Scale letter type
Expand leading/tracking

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