This is the 373rd most frequent French word.
compter
To count; to rely on.
In this sentence, 'compter' is used to mean 'plan' or 'intend', expressing the speaker's intention to do something.
Je compte partir demain matin.
I plan to leave tomorrow morning.
Here, 'compter sur' means 'to rely on or trust in', demonstrating dependence or trust in someone or something.
Elle compte sur son ami pour l'aider.
She relies on her friend to help her.
In this example, 'compter' is used literally to mean 'to count', referring to determining a number.