The simplest summary is this:

Many Bitcoin services and users encounter complexities because they have to (should) generate a new send / receive address for every transaction. They attempt to eliminate this by reusing a single address…however they introduce risk as they compromise their privacy, since all transactions related to this address can easily be identified and analyzed.

Silent payments aim to solve these challenges. They use static addresses intended to be reused, while transactions made to them can only be identified by the sender and the recipient.

(Adapted and paraphrased from https://bitbox.swiss/blog/understanding-silent-payments-part-one/ )