Digital certificates are the digital equivalent (i.e. electronic format) of physical or paper certificates. Examples of physical certificates are driver's licenses, passports or membership cards. Certificates serve as identity of an individual for a certain purpose, e.g. a driver's license identifies someone who can legally drive in a particular country. Likewise, a digital certificate can be presented electronically to prove your identity or your right to access information or services on the Internet.
Cryptography is the science of enabling secure communications between a sender and one or more recipients. This is achieved by the sender scrambling a message (with a computer program and a secret key) and leaving the recipient to unscramble the message (with the same computer program and a key, which may or may not be the same as the sender's key). There are two types of cryptography: Secret/Symmetric Key Cryptography and Public Key Cryptography
The emphasis of cryptography is on data confidentiality, data integrity, sender authentication, and non-repudiation of origin/data accountability.
The Public key infrastructure (PKI) is the set of hardware, software, policies, processes, and procedures required to create, manage, distribute, use, store, and revoke digital certificates and public-keys.
It's a process to ensure that a message does not originate from someone other than its purported sender. Sender authentication is achieved through two related mechanisms: digital signature and digital certificate.
Encryption is the transformation of information from readable form into some unreadable form.
Decryption is the reverse of encryption; it's the transformation of encrypted data back into some intelligible form.