<<umlaut is a little like turkish vowel harmony. that is, umlaut is an
attempt at vowel harmony. it is when a vowel changes in pronounciation
to approximate another vowel, it moves closer to that vowel.>>
The important difference is that umlaut is regressive (right to left),
while vowel harmony in Turkish is progressive (left to right).
But I don't think that Turkish is the best way to route to answering
the basic question. There have been very good answers already, but I
will try to add another.
Umlaut is a process that happened in the history of most Germanic languages.
There was a tendency to make vowels similar in some way to the vowels
FOLLOWING them, in the next syllable.
In some of the older languages (to a fair extent this is true of Old
Norse) you can look at umlaut as a "living" process. You can regularly
expect to see the vowel in the root of a word change if a certain kind
of vowel follows in the next syllable.
I speak of living and dead processes. A process if living if we can point
to a workable rule that tells us when a change happens. There will be
some exceptions, perhaps, but not a great many.
The vowels that have made changes relevant in Old Norse are /a, i, u/,
so we speak of i-umlaut etc. When you learn Old Norse you should learn
some rules about when vowels can change becuase of a /a/, /i/, or /u/
in the following syllable.
There are many traces of i-umlaut in Modern German, but the process doesn't
work phonetically any more. You have to know whether any particular word
"takes" umlaut or not--like when you learn the plural of nouns. The use
of "umlaut" for the little marks (diaresis) is just a shorthand. Don't
confuse this with the historical process of umlaut. When you study modern
German (as a foreigner) you have to memorize some facts about "umlaut."
There are no rules--it's memorization only. That's because umlaut is
"dead" in Modern German, although there are numerous traces of historical
"i-umlaut."
In English, we have traces of i-umlaut in noun pairs like foot/feet mouse/mice
etc. These are NOT "living" examples, because we can't say WHY this happens,
without studying the history of the English language. When you do study
Old English, you see these are all due to "i-umlaut," and that there
used to be many more pairs like this. The plural of "book" could have
been "beek" instead of books! There was also some u-umlaut in Old English,
but it hasn't left any traces in Modern English.
ABLAUT--nothing to do with umlaut. Only sounds kind of the same, because
of the German word "laut" used to form both.
Ablaut is much older. It involves changing vowels in line with changes
in grammatical meaning--like verb tenses. This is the kind of thing English
has in "ride, rode, ridden." There are seven classes of these "strong"
verbs in Old Norse and Old English. Modern English and German have some,
but not so many verbs, and not so many classes. But this was a "dead"
process even in Old Norse or Old English. They weren't adding new verbs
to any of these classes, and there was no "rule" for knowing what verbs
would have ablaut and what verbs wouldn't.
Hope this helps. I know sometimes different answers to the same question
can provide a variety of "light."