An enharmonic equivalent is a pitch or tone which can be spelled with two or more different letter names.
For example, looking at the keys of a piano we can see that one
half step above the note G is the note G-sharp.
However, this very same key, the one that we just identified as being the note G-sharp, is also a half step below the note A.
Therefore, in addition to being called G-sharp, this note can also be spelled with the letter name A-flat. Now, because we are able to call this same exact pitch by two different letter names, the note G-sharp and the note A-flat are therefore considered to be enharmonic equivalents.
In that same respect, one half step above the note D is the note D-sharp.
Just like in the previous example, we can see that this same key is also one half step below the note E.
Therefore, in addition to being the note D-sharp, it can also be spelled by the letter name E-flat. With this in mind we can see that the notes D-sharp and E-flat are enharmonic equivalents. This is in fact true for all of the black keys on a piano.
However it is important to know that it's not only the black keys which can have enharmonic equivalents. Sometimes certain enharmonic equivalents are not as obvious.
Because the notes B natural and C natural are separated by a single half step there is no black key in between them.
Knowing that a flat lowers a note by one half step, because B is one half step behind the note C the key in which we typically refer to as being the note B natural can also be referred to by the letter name C-flat
In other words, the note B natural and the note C-flat are enharmonic equivalents.
On the contrary, because a sharp raises a note by one half step, and the note C is a half step above the note B, B-sharp is then the enharmonic equivalent of the note C.
The same is true for the notes E natural and F natural.
Because F natural is a half step above the note E natural,
the note E-sharp is the enharmonic equivalent of the note F natural.
And because E natural is a half step below the note F natural, the note F-flat is the enharmonic equivalent of the note E natural.
Now, the way you spell a pitch often depends on two important factors; the key in which the note is being played, and what is happening around the note in the music.
For instance, when you are in the key of G Major this pitch is called F-sharp, not G-flat.
Even though the notes F-sharp and G-flat are enharmonic equivalents and are technically the same exact pitch, when playing a scale you do not want to repeat letters. Rather, it is important to maintain the proper alphabetical order.
Playing a G Major scale as G - A - B - C - D - E - Gb - G not only skips over the letter F it also repeats the letter G. Therefore, in this situation it is more appropriate to use the letter name F-sharp rather then G-flat.