What is the significance of the ritual of deliverance?

Deliverance is primarily aimed at the living rather than the dead. When Shakyamuni Buddha taught the Dharma, he preached it to the living, so that we use wisdom to deliver ourselves. Nonetheless, rituals for the dead can bring them merit, and on hearing the Dharma they may be able to let go and achieve deliverance, attaining rebirth to the Western Pure Land or to a better realm.

What is the purpose of the "Releasing Burning Mouths" ritual?

What it really means to make offerings?

Making offerings is a very important part of Buddhist practice. To make offerings is to practice giving, one of the six perfections. It benefits both ourselves and others in that through giving we are actually repaying the kindness of others and showing gratitude, as well as learning and growing spiritually. Also, by making offerings to the sangha we are contributing to spreading the Buddhadharma and helping others engage in spiritual practice, thereby gaining great merit.

What is the significance of offering pure meals?

When we offer pure meals for practitioners engaged in pure practice to eat at prescribed pure times, we acquire merit and create affinities in the Dharma. Many people do this to fulfill or redeem a vow.