I have been absence for some time due to several photo assignments but I am back to explain how to use your already Level tool knowledge to understand the power of the curves.
After opening the Curves dialog from either the Image >> Adjustments menu or from the New Adjustment Layer icon (the half black, half white circle icon) on the Layers palette reveals the Curves window.

The "curve" of Curves isn't there until we make it. What we have to start with is a grid that looks at least somewhat like Levels with a diagonal line running from the lower left to the upper right. This diagonal line will become our curve.
As with Levels, the x-axis represents the range of brightness in the image from black to white. Rather than a count of how many pixels fall at each value though, the y-axis here represents how bright a pixel of the resulting image should be when we click "OK." The diagonal line shows that every tonal value should remain unchanged -- zero maps to zero, 255 maps to 255 and so on. Photoshop doesn't show us a graphical representation of our image data in the grid but rather a function showing how that data will be changed by Curves.
If we go up from any given value on the x-axis until we hit the diagonal, the go over to the y-axis, we're at the same brightness we started with. In other words, every input value will map to the same output value. In order to actually make a change, we have to move and bend that diagonal line to re-map input values as we want them to end up.
Let's start with black point and white point adjustments, just as we did for Levels. At opposite ends of the diagonal line mapping input to output tones you will find a small dot. Grab hold one of this dots with your mouse and drag it around and you will see the image change (assuming the Preview option is checked in on the bottom right of the dialog box). The original diagonal line also changes. This line is our curve. Don't worry if it still seems like nothing but straight line segments so far. We'll start bending it more later on. No matter what, the curve always stretches
from the far left to the far right. It has to so Photoshop knows how to convert input values over the entire 0 to 255 range. If it doesn't also stretch all the way from bottom to top, the output values (the results of our Curves adjustments), will only cover part of the 0 to 255 range and the image will not have a correspondingly low contrast.
When we adjusted the black point in Levels, we moved the slider to the right such that pixels in our image that used to not be black became black. That is, we set the black point by selecting the original value (input value) we wanted to map to black (output value) when we clicked "OK." The Input Levels above and Output Levels below the Levels histogram reinforce this concept. Since we didn't mess with the Output Levels when we set Levels, we were always mapping our selected Input Black Point to 0 which is, of course, black.
In Curves, we can set the black point by dragging the original (0,0) point (the one on the lower left end of the starting diagonal) to any point along the x-axis at the bottom of the graph area. As we move the point, we can see the corresponding Input and Output numbers in the area below the curve. So long as we stay at the bottom edge of the area, the output level will remain at zero since we have picked a point at the lowest possible value on the y-axis of Output values. We can similarly pick a white point by moving the (255,255) point (the one on the top right of the original diagonal) to any point along the top of the graph area. The modified image will have greater contrast than it did to begin with since we moved the black point and white point inward.
For the most part, we will still have a straight line stretching from Output values 0 to 255 (bottom to top), much as we did before we adjusted anything. However, this revised line (curve) will have a steeper slope than did the original. This is a fundamental concept in understanding Curves: steeper slopes mean greater contrast. If we had moved the original (0,0) and (255,255) points up and down along the left and right sides instead, we would have created a line with a shallower slope, and thus an image with lower contrast.
It can be worthwhile keeping an eye on the Histogram palette while adjusting Curves. If you don't already have it enabled, you can do so via Windows >> Histogram on the menu. Using it will help keep you informed of what you are doing to your image as you make your adjustments.
The Curves equivalent of setting the Gray Point slider involves adding an additional control point on our curve (up to now, actually just our diagonal line). If you click anywhere along the curve, you will add a point. It will show up as a solid dot and all other points including the two original ones will become open circle dots. No matter how many points your curve has, only one of them is active at any given time. To switch from one point to another existing point, simply re-click on it. If you pull this new point slightly upwards, the curve will finally curve, creating an arc between the two endpoints we made by adjusting black and white points (or the original two endpoints if we decided to set black and white points via Levels). Don't go overboard; a little movement of the point goes a long way as you will be able to tell by watching the image itself as well as the Histogram palette. This brings us to our next fundamental concept: easy does it. Drastic amounts of movement in Curves will do nothing more than create bizarre images. Pulling a point in the middle of the curve upward is equivalent to moving the Levels gray point slider towards the left, increasing the overall brightness of an image. Pulling it slightly downward instead is the same as moving the Levels gray point slider to the right, making the image seem somewhat darker overall. If you need to delete a point, simply drag it off the graph and it will go away.
To illustrate what we've been discussing, take a look at the image above on the right. This is an unmodified shot of a sentry box in San Juan Puerto Rico. Reasonably nice, but somewhat lacking in impact and a tad underexposed. Now look at the second version of this same image shown below.
Keywords:curves tools, ajusting, correction, photoshop, brightness, curves adjustments, contrast.

Original Image

Used Curve

Adjusted Image Using Curves