Accidentals are signs used to raise or lower notes by half steps.
A half step is the distance between two adjacent keys on a piano keyboard. In music theory, the distance between two notes is called an interval.
A half step is the smallest musical interval in music. (It is called a semitone in British English.)
A whole step is the distance equal to two half steps. (It is called a whole tone in British English.)
Sharps and Flats
A Sharp is an accidental that raises a note by a half step.
A Flat is an accidental that lowers a note by a half step.
Double Sharps and Double Flats
To raise a note by a half step means moving to the right to the next adjacent key on the piano keyboard. To lower a note by a half step means moving to the left to the next adjacent key.
For example, a half step higher than C on a piano keyboard is the black key immediately to the right of C. The note name is C sharp (C♯).
C sharp (C♯) is half step above C. On the staff, the Sharp ♯ symbol is placed to the left of the C note to raise the C note by a half step, making it a C sharp (C♯).
Since, the same pitch on the piano keyboard can have more than one musical note names, the same black key that represent C sharp can also be called D flat (D♭). A half step below D is D flat, which is the black key immediately to the left of D. D flat share the same black key as C sharp.
These two notes are called the enharmonic equivalent or enharmonic notes. The enharmonic notes are notes that share the same pitch and sound exactly the same when played on a piano, but have two different musical note names.
Natural notes, sharps and flats on a piano keyboard:
The Natural Sign
The natural symbol ♮ is an accidental which cancels out any previous accidental. Whenever you see a natural symbol placed to the left of the note, it means the note is not longer a flat or a sharp. The natural symbol applies only to the note for the rest of the measure.
For example, the key signature of G major scale has one F sharp. The key signature indicates that all F notes are sharp. If a natural symbol is placed before a specific F note, that F note is to be played as the natural F for the rest of the measure. After the measure ends, all F notes are to be played as F sharp again.