Everybody is talking about it, but what does it mean?

Look at your thermostat. It is measuring the current room temperature. If it is to low, heating will be started. It is measuring again. If the current temperature is to high, heating will be stopped.

Agile is continuous

It is a “continuous measurement and control technology“. The thermostat example is a practical implementation of the PDCA (plan–do–check–act) method. See more Details here: https://en.wikipedia.org/wiki/PDCA

Agile is empirical

Agile is based on empiricism. The Three Pillars of Empiricism are are: transparency, inspection and adaption. See more Details here: https://www.scrum.org/resources/blog/three-pillars-empiricism-scrum

Agile is a mindset

Agile is based on core principles revealed by the agile manifesto. But before quoting it, I want to refer to a(nother) brilliant definition:

A(nother) definition

Agile is the ability to create and respond to change. It is a way of dealing with, and ultimately succeeding in, an uncertain and turbulent environment.
Agile software development is an umbrella term for a set of frameworks and practices based on the values and principles expressed in the Manifesto for Agile Software Development and the 12 Principles behind it.
Agile101

Now it is for sure time to quote the source of wisdom:

Manifesto for Agile Software Development

We are uncovering better ways of developing software by doing it and helping others do it.
Through this work we have come to value:
Individuals and interactions over processes and tools
Working software over comprehensive documentation
Customer collaboration over contract negotiation
Responding to change over following a plan
That is, while there is value in the items on the right, we value the items on the left more.
https://agilemanifesto.org

12 principles

We follow these principles:
Our highest priority is to satisfy the customer
through early and continuous delivery
of valuable software.
Welcome changing requirements, even late in
development. Agile processes harness change for
the customer’s competitive advantage.
Deliver working software frequently, from a
couple of weeks to a couple of months, with a
preference to the shorter timescale.
Business people and developers must work
together daily throughout the project.
Build projects around motivated individuals.
Give them the environment and support they need,
and trust them to get the job done.
The most efficient and effective method of
conveying information to and within a development
team is face-to-face conversation.
Working software is the primary measure of progress.
Agile processes promote sustainable development.
The sponsors, developers, and users should be able
to maintain a constant pace indefinitely.
Continuous attention to technical excellence
and good design enhances agility.
Simplicity–the art of maximizing the amount
of work not done–is essential.
The best architectures, requirements, and designs
emerge from self-organizing teams.
At regular intervals, the team reflects on how
to become more effective, then tunes and adjusts
its behavior accordingly.
https://agilemanifesto.org/principles.html