What does a gradient mean in physics? I'm a physics high school student and have learned about the term 'gradient' regarding a few situations, such as pressure gradients and temperature gradients.
But what does this really mean? What is the physics meaning of gradient? I know that the pressure gradient is $\frac{dP}{dx}$ and the temperature gradient is $\frac{d\theta}{dx}$. If we take the $dx$, for instance, as an extremely small number, then the gradient approaches towards a very large value. What does this imply? Please explain in simple language!
 A: I struggled with the concept myself even in later calculus (where 2 and 3-dimensional gradient operators are developed)... which is a real problem when a meteorology major!
But one day it just dawned on me that it's as simple as it sounds.  It's the rate of difference.
As Gary mentioned, in one dimension, a gradient is the same as a slope.
As you indicated, in $\frac{dP}{dx}$, if you decrease $dx$, it would seem mathematically to be pushing the result to larger values.  But in actuality, when you consider a smaller $dx$ (distance), you also will consequently see a smaller change in the property of interest (pressure in this case).
It's exactly like working with a line... if you have a slope of $2$, you have a slope of $2$ regardless of the scale you look at it on.  If you look at a smaller $x$ change in the line, say $dx = 0.01 \ldots$ then the $y$ changes follow suit, and $dy$ is just $0.02$.  They vary together.  $\frac{dy}{dx}$ is a ratio.
It also helped me to step back and reconsider the concept/meaning/definition of derivatives again.  Remember, $dP/dx$ is just $\frac{\Delta P}{\Delta x}$.  Except applied at an "instantaneous" spot.  Typically we still calculate $\frac{dP}{dx}$ observationally using $\frac{\Delta P}{\Delta x}$.  It's just that in the real world, things usually don't vary consistently (linearly); some spots have a "quicker" change than others, such the temperature gradient across a cold front.  So $\frac{\Delta P}{\Delta x}$ doesn't take into account variations in the slope itself, so we transition to $\frac{dP}{dx}$ ideally for perfection.  Even when we're incapable of obtaining such a perfect value outside of theoretical/derivation circumstances.  But it's still the same basic idea either way: how "quickly" the value ($P$) changes over a given direction ($x$).  
It was frustrating to wrap my head around.  But spend enough time staring at a weather map or thinking about it as you climb complex terrain, and I think you'll really understand that we don't pick $dx$, but that $\frac{dy}{dx}$ is truly just one quantity just like a slope, linking the two variables together.  And I'm confident it will suddenly click innately what a gradient means! (even in 2-D or 3-D... that just adds a direction in which the gradient changes)
A: Gradient refers to how steep a line is, which is basically the slope.
$\frac{dP}{dx}$ and $\frac{d\theta}{dx}$ are basically the derivative of a function, i.e its slope. 
The easiest way to determine slope is to graph the function, then observe the  x coordinate of a point on the graph and its respective y coordinate. If the y coordinate is increasing as the x coordinate is increasing, the slope /gradient is said to be positive at that point and if the y coordinate is decreasing as the x coordinate is increasing, the slope is said to be negative. 
A: What I know from the basic is that..
Gradient is a slope of a curve in a graph at specific points on the curve.
If a curve is linear then gradient remain constant.
If it is a curve then gradient vary.
