What is the intuitive meaning of uncorrelated?

"Uncorrelated" means that as one of the two variables increases, on average the other one does not increase or decrease.

That does not mean they are independent: for example, suppose the two variables are the $x$- and $y$-coordinates of the point $(x,x^2)$ where $x\in\{-1,0,1\}$, each with equal probability. If you know $x$, that determines $y$, so they are not independent, but they are uncorrelated.

The images below are scatterplots with respective correlations $0.99$, $0.95$, $0.9$, $0.7$, $0.5$, $0.3$, $0$, $-0.3$, $-0.5$, $-0.7$, $-0.9$, $-0.95$, $-0.99$. The one case in which the correlation is $0$ is the case in which the two variables are uncorrelated. If the correlation were exactly $1$ or exactly $-1$, then all of the points would lie on a single straight line.

correlation $=0.99$:

$=0.99$" />

correlation $=0.95$:

$=0.95$" />

correlation $=0.9$:

correlation $=0.7$:

$=0.7$" />

correlation $=0.5$:

correlation $=0.3$:

$=0.3$" />

correlation $=0$:

$=0$" />

correlation $=-0.3$:

$=-0.3$" />

correlation $=-0.5$:

$=-0.5$" />

correlation $=-0.7$:

$=-0.7$" />

correlation $=-0.9$:

$=-0.9$" />

correlation $=-0.95$:

$=-0.95$" />

correlation $=-0.99$:

$=-0.99$" />