Spacetime is (apparently) very very close to being flat overall. There may be local anomalies, but over large distances those in the know claim it to be either flat or only very slightly curved either positively or negatively. (A bit like saying the earth is positively curved, but locally - e.g. on the open sea - it looks flat, but can look negatively curved in some other localities - e.g. in a pringle-shaped valley.)

It's easy to visualise what a curved two-dimensional surface means, because we can see & think in 3 dimensions. So when someone tells us the earth is round, we can visualise it (even though to us it locally looks flat).

The problem with visualising the curvature of 3-D space (or 4-D spacetime) is that you need to be able to visualise in 4-D (or 5-D) space in order to picture what it means - i.e. you need to be able to think in at least one higher number of dimensions than the surface/volume whose curvature you're trying to describe.

But it can be done mathematically. In 2-D space, the angles of a triangle always add up to 180 degrees ... if the space is flat. But if it's curved, and if your triangle is big enough, then the angles will add up to either more than (positive curvature) or less than (negative) 180 degrees.

And so the curvature of spacetime can be described mathematically by saying that the angles of a (very, very) large triangle plotted in spacetime would have angles either less than or greater than 180 is spacetime isn't flat.

Or I think that's the case, anyway. Maybe.