The ear perceives frequencies that have ratios that are whole multiples of the fundamentals as being specially related (a condition known as the musical octave). For example, since concert A is 440 Hz (A3), the ear hears 880 Hz (A4) as being the next highest frequency that sounds most like concert A. The next related note above that will be 1760 Hz (A5). Therefore, 880 Hz is said to be one octave above 440 Hz, and 1760 Hz is said to be two octaves above 440 Hz, etc.
Since these frequencies are even multiples of the fundamental, they’re known as "even harmonics". Not surprisingly, frequencies that are odd multiples of the fundamental are called "odd harmonics". In general, even harmonics are perceived as creating a sound that is pleasing to the ear, while odd harmonics will create a dissonant, harsher tone.