What it means
I don't understand. 懂 means to comprehend, not just to hear.
When to use it
Pair it with 我听不懂 (wǒ tīng bù dǒng) if the problem is listening specifically. Both are useful in the first weeks of learning.
Examples
duì对bu不qǐ起，wǒ我bù不dǒng懂。
Sorry, I don't understand.
zhè这ge个wǒ我bù不dǒng懂，qǐng请jiě解shì释yī一xià下。
I don't understand this, please explain.
wǒ我bù不dǒng懂zhōng中wén文。
I don't understand Chinese.
The full set of survival phrases for greetings, dining, shopping, and getting around, each with audio.