This is the 17866th most frequent Russian word.
успехам
"Успехам" means "successes" (dative plural form).
In this sentence, 'успехам' is in the dative case, indicating the indirect object of the verb.
Я радуюсь вашим успехам.
I am pleased with your successes.
Here, 'успехам' is in the dative case, showing association or addition to the successes.
Он присоединился к нашим успехам в проекте.
He joined in our successes in the project.
In this sentence, 'успехам' is also in the dative case, marking the entity to which something is owed.