Why is it so important, whats the big deal?

The main reason GDPR is so scary are the potential financial penalties - €20 Million or 4% of previous years annual turnover, whichever is higher.
Enough to scare most companies, whether large or small, so most are taking this seriously.
Going back to your website compliance, there are a number of rules and regulations which need to be adhered to, each falling into different areas:

Consent

Ensuring individuals can opt in for data to be gathered

​Processing

Defining rules about the processing of personal data

Securing data

Ensuring organisations protect an individuals privacy

Breach notification

Informing individuals (and the authorities) about data breaches

Right to access

Adhering to requests for access to personal information held

Right to be forgotten

Ensuring individuals can be removed for your records

Due process

​Ensuring you have defined procedures to follow and individuals responsible for actioning them