which purpose are router solicitation and router advertisement used?

https://tools.ietf.org/html/rfc4861

Router Solicitation: When an interface becomes enabled, hosts may
send out Router Solicitations that request routers to
generate Router Advertisements immediately rather than
at their next scheduled time.

Router Advertisement: Routers advertise their presence together
with various link and Internet parameters either
periodically, or in response to a Router Solicitation
message. Router Advertisements contain prefixes that
are used for determining whether another address shares
the same link (on-link determination) and/or address
configuration, a suggested hop limit value, etc.