This is the 6223rd most frequent Russian word.
трогать
To touch.
In this context, 'трогать' is used to mean 'to address or handle', applied in a non-physical sense.
У меня нет времени трогать этот вопрос сейчас.
I do not have time to deal with this issue right now.
The word 'трогай' from the verb 'трогать' means 'touch' in this imperative sentence, indicating a physical action.
Не трогай мою книгу.
Do not touch my book.
The verb 'трогать' here is used figuratively to mean 'to emotionally move or affect' someone.