Take a look at this picture of a keyboard. If you read the notes from left to right, you will notice that the notes are getting higher. The first note on the left is a C, and C♯ which is a half step higher, is its closest neighbor.

As you read the notes from left to right (C, C♯, D, D♯, E, F …) you will notice that each black key shares a letter name with the white key to its immediate left.

The pattern that you are reading – moving up by half steps, alternating between white and black keys – is called a chromatic scale.

Now find the C closest to the right side of the picture. Read the pattern backwards, from right to left. Notice that the black notes are now labeled with flat signs. As you follow the chromatic downward (C, B, B♭, A, A♭, G …) you will notice that the black keys share a letter name with the white key to its immediate right.

What this means is that every black key can go by two names. The black key that sits between C and D can be called C♯ or D♭. The note sounds the same no matter what you name it.
 

When a note goes by two names but sounds the same, those two names are called enharmonic equivalents. This image shows a C chromatic scale with all of its enharmonic equivalents in brackets.