A meme is "an idea, behavior or style that spreads from person to person within a culture." A meme acts as a unit for carrying cultural ideas, symbols or practices, which can be transmitted from one mind to another through writing, speech, gestures, rituals or other imitable phenomena.

An example of a meme would be Overly Attached Girlfriend. You can see references and examples of OAG without the need of it's image macro.

The image macro of Overly Attached Girlfriend is the picture of her with buggy eyes looking at the camera (taken from her Justin Bieber "Boyfriend" parody on YouTube).

Sometimes, as in the case of OAG, the terms 'image macro' and 'meme' can be used interchangeably. However, not all memes have image macros, and not all image macros have memes.

For instance, the OP's image macro here is not a meme. It isn't a funny idea that spreads, it is just a picture with text. No one would understand what I am saying if I talked about the "hairy wizard" meme, but they would understand if I told someone "I saw an image macro in which Harry responded to Hagrid's famous 'You're a wizard, Harry' with 'You're a hairy wizard'."

Likewise, as I mentioned, not all memes have image macros. A good example of this is planking. Other examples include taking an arrow to the knee, Chuck Testa, and Nyan Cat. These all have one thing in common: People know what they are (meme) but aren't necessarily spread through image macros (like Arrow to the Knee can be spread through the comment "and then I took an arrow to the knee" instead of having to post an image like this.