You asked in a comment for a physical meaning.
So, you are accelerating away from the Earth because there is a pressure on you, the force on your feet if you're standing, which is not balanced by any other force. Gravity is no longer considered a force, therefore you are accelerating.
Where does this force come from? Well, this is not really a property of mass, but rather a property of electrons “wanting” to take up space because they cannot be in the exact same state as each other. This is called the Pauli Exclusion Principle, when you bring electron clouds too close they repel.
Gravity is not a force per se in general relativity but it does still bring matter into close proximity, from which it can repel other matter.
“OK but isn't this just a difference in a mathematical description of who accelerates and who stays stationary?”—no, it does make a difference, because of relativity. Special relativity makes one core claim about reality from which all of its weirdnesses can be derived, and it is a claim about acceleration, which you can phrase like this:
It is a universal property of acceleration that whenever you accelerate in some direction “forwards” by some acceleration $\alpha$, in addition to all of the normal Doppler shifts that you expect classically, there is an anomalous Doppler-like effect tied to acceleration: you will see any clock ahead of you by coordinate $x$ (negative if behind you) ticking at a rate of $1+\alpha x/c^2$ seconds per second.
Concretely, imagine I stand under a geosynchronous satellite. If we are both in the Newtonian state of force balance with no acceleration, then I will say that its clocks and my clocks are ticking at the same rate. But if gravity is a fictitious force and we are both actually accelerating upward constantly, I will say that the satellite's clock ticks faster, and the satellite will say that my clock ticks slower ($x$ being negative for the satellite), and we will therefore agree that there is a “gravitational time dilation.”
(This also causes lensing but you really want to make this more geometrical rather than phenomenological to describe that.)
This has been observed in experiments and actually needs to be constantly corrected for in the GPS satellites, which work by broadcasting times to the Earth and then your phone triangulates where it is based on microsecond differences in the times it receives at once, plus models of where those satellites should be in relation to Earth's surface. The tick factor $\alpha x/c^2$ is about two parts per billion for these satellites ($\alpha = g$, $x$ = 20,000 km) so it can cause offsets of microseconds after an hour or two. So their atomic clocks actually are calibrated to tick slower by two parts per billion to avoid falling out of sync with Earth's surface.