Plenty of books have been written about digital certificates, so we won't go too deep into the concept, but it's important to lay down some ground work, so that we are all on the same page about this topic.
PKI stands for Public Key Infrastructure, and this refers to the keys used to encrypt and decrypt data that is exchanged between computers over a non-secure medium such as the public internet. The science of encrypting data goes back a long way. (Remember using Pig Latin as a kid? Esyay, atthay isway away udecray ormfay ofway encryptionway!)
Encryption is based on a simple concept. You want to send data to someone without anyone else being able to read it. You take the data, and change it in a way that only you and the future recipient know. If that data falls into the wrong hands, it will look like meaningless garbage. The intended recipient, though, knows how to reverse the process and read it.