G-d spoke to Moses, saying, "Command the children of Israel, You must guard My offering, My food for My fire-offerings, a spirit of satisfaction for Me, you shall take care to offer to Me at its appointed time."
G-d calls the sacrifices His daily "food," for just as food sustains the body, so did the sacrifices draw sustaining Divine life-force into the world. Furthermore, the constancy of the daily sacrifices expressed the eternal bond between G-d and the Jewish people.
The daily prayers were instituted to parallel the daily sacrifices and to substitute for them in the absence of the Tabernacle or Temple. Thus, our daily prayers also "sustain" G-d.
If we ever doubt how important our prayers can be, we should recall that G-d considers them vital to the world's existence and maintenance.
They are as important to Him as our daily bread is to us.