If you get signed material, you may want to verify the signature.
Digital signatures usually are created using a private key and can be verified using the associated public key.
Certificates essentially are transport containers for public keys with some extra information. Thus, to verify signatures you usually need the certificate of the signer.
You install certificates to make them known to your system (to allow for signature verification) and to tell your system to trust material signed by the associated private key.
As having to install certificates by each and every party you want to trust is too much work, certificates can have hierarchies, some root certificate may be the issuer of multiple other certificates, and by trusting that root you implicitly trust those other certificates the root issued.
For more details you may want to ask on https://security.stackexchange.com/.