To ensure you don't get lost in a jumble of photo jargon, here's a primer on what the Instagram editing tools actually do:
Brightness: Pretty straightforward, this can brighten up a dark image and darken a bright one
Contrast: When turned up, it exaggerates the darks and lights in an image, and softens them when turned down
Saturation: Increasing this adds strength/intensity to the colors in your image, and vice versa
Warmth: Turning this up brings out "warm" colors (oranges, red, and yellows, generally); turning it down brings out "cool" colors (like blues, purples, and greens). This tools can be used to change the mood of a photo, or to bring colors into balance.
Sharpen: Turning this up focuses and clarifies your image and makes everything a little crisper
Highlights: Adjusting this will affect all of the brightest parts of your image -- bumping it up will make the brightest parts of your image even more vibrant, and moving it down will bring down the brightness in those sections to reveal more detail in them that may have been washed out by excessive light. This can be a huge help if a particular section of your image is blown out by a too-bright light source or the sun.
Shadows: This does essentially the same thing as Highlights, but for the dark areas of an image. So turn it up to see what's hiding in the shadows, or turn it down to darken.