Complex sentence: ASCE provides peer reviews at the request of public agencies and projects as a "means to improve the management and quality of (public agency) services and thus better protect the public health and safety with which they are entrusted".
Split into simpler sentences: ASCE provides peer reviews at the request of public agencies and projects. Peer reviews are "a means to improve the management and quality of (public agency) services and thus better protect the public health and safety with which they are entrusted".