Hålla tummarna means "to hold one's thumbs" and is used to wish someone luck. So, if you tell someone you're holding your thumbs, it's the same as saying, "I'm crossing my fingers for you!" or simply "I'm wishing you luck!" in English.

Source: Linnea, OLS Community Manager
Hålla tummarna: Pronounced as [Hohl-lah tuhm-mahr-nah].
Crossing one's fingers is an old Christian symbol. Centuries ago, people would form a cross with the index fingers of each hand to ward off bad luck. But holding one's thumb is an older gesture, believed to date back to the Roman Empire.
You can follow the phrase with "för" and a noun, or "att" and a verb, for example, jag håller tummarna för min vän (I'm keeping my fingers crossed for my friend) or jag håller tummarna att det ska hända (I'm crossing my fingers that it happens).
So why thumbs? This is an example of an interesting linguistic divide. In England and many parts of Europe (France, Spain, and Sweden's neighbours Norway and Denmark), crossing one's fingers is a sign of wishing luck.
If you get confused by this phrase, you can say "lycka till!" instead, which means good luck.
Example:
Jag ska hålla tummarna hela dagen.
I'll be crossing my fingers/wishing you luck all day.
Nu måste vi hålla tummarna!
Now, we have to cross our fingers/hope for the best!
Linnea, OLS Community Manager – Swedish