Diphthongs are types of vowels where two vowel sounds are connected in a continuous, gliding motion. They are often referred to as gliding vowels. Most languages have a number of diphthongs, although that number varies widely, from only one or two to fifteen or more.
A vowel is a specific type of sound, characterized by a lack of full obstruction to the air flow. Vowels can be contrasted with consonants, where there is such an obstruction. As air comes out when you are speaking a consonant, there is a build up of pressure as the air flow is constricted. When speaking a vowel, there is no built up pressure, the sound is simply shaped by the position of the tongue.
Vowels are generally characterized by three different criteria: the position of the tongue in the mouth relative to the roof of the mouth (height), the position of the tongue in either the front or back of the mouth (backness), and the shape of the lips as the vowel sound is being made (roundedness). There are other things that may characterize vowels, but they are not very common in English — things such as the position of the root of the tongue, for example, rarely affect English vowels, though they affect the vowels in many African languages.
When vowels come together, they may either be two distinct syllables, or may merge into one syllable. When they merge, they form what are known as diphthongs. If they stay separate they are simply two monophthongs. An example of two single syllable vowels can be seen in the word triage, in which the i and the a are both pronounced on their own. An example of a diphthong can be seen in the word mouse, in which the ou part of the word obviously consists of two distinct vowels, but there is no syllabic break between the two.
Diphthongs can usually be seen as having two distinct parts — the nucleus, and the off-glide. The nucleus of the diphthong is the vowel that is most stressed, and forms the center of the sound, while the off-glide is the vowel which seems to flow into or off of the nucleus vowel.
The three major diphthongs in Standard English, which are known as phonemic diphthongs, areai, aw, and oy. All three of these diphthongs are very common, and many people simply think of them as single vowels in some contexts. For example, in the English word ride, the i would be transcribed phonetically as ai. Although it appears as a single letter in our writing, it actually consists of two vowels — if you say the word you should be able to hear the two. Similarly, the word how contains the diphthong aw at the end, and the word boy contains the diphthong oy.
Other diphthongs in Standard English are the ei sound in the word fame or the pronunciation of the letter a, and the ou sound in the word phone. Other languages have many more diphthongs aside from these, and other dialects of English may have more diphthongs as well. Languages such as Finnish have nearly twenty diphthongs, while the Received Pronunciation dialect of English has an extra five or so diphthongs not found in Standard English.
In addition to diphthongs and monophthongs, there are also what are called triphthongs. These are similar to diphthongs, but instead of moving simply from one vowel sound to another, a third sound is also added. (references from www.wiseGEEK.com/what-are-diphthongs.htm)