Questions & Answers about Она кивнула, и я сразу всё понял.
Кивнула is the past tense form of the verb, because the sentence describes something that already happened.
The dictionary form is кивнуть = to nod.
In Russian, past tense forms change for gender and number:
- кивнул = he nodded
- кивнула = she nodded
- кивнуло = it nodded
- кивнули = they nodded
Since the subject is она (she), the verb has to be кивнула.
For the same reason: Russian past tense agrees with the subject in gender and number.
Here, the subject is я (I), but Russian past tense still shows gender:
- я понял = I understood / I got it (male speaker)
- я поняла = I understood / I got it (female speaker)
So я сразу всё понял tells you the speaker is male. If the speaker were female, it would be:
Она кивнула, и я сразу всё поняла.