A quote from the Dalai Lama

Petitioning those who possess the three jewels [Buddha, Dharma and Sangha] evokes their compassion-not by generating it in them, but by opening yourself to it.


In other words, by praying to highly realized beings (in any tradition), we are able to receive help. Not because they are unwilling to help otherwise, but because we shut ourselves off from the help, and the prayer helps us to be open to it. If you pray for another being's benefit, that's also primarily benefiting you. If I have the power to cut myself off from the help of all the Buddhas and bodhisattvas who have aspired to liberate sentient beings, then people who I pray for certainly also have that power. The prayer might be able to help them, but just as physical acts can be rejected, so can spiritual acts. Also, just as I can't lift a weight that's too heavy, by prayer alone I can't, for example, stop someone from becoming ill and dying. This is even beyond the Buddha's power. Everyone needs to contend with the force of their own karma, and although the Buddhas can help, this is only if the person develops their mind to receive the help. That's why the emphasis in Buddhism is on liberating all sentient beings. We need to give everyone the tools so that they can personally transform their suffering. Praying on their behalf is not enough, alhtough it does have an effect. The only way to give everyone these tools is to first get them yourself-thus, the personal aspiration to achieve Buddhahood for the benefit of all sentient beings.