I-MUTATION (also known as "i-umlaut") is the raising and fronting of a root vowel in anticipation of "i" or "y" sound in a suffix.
This sounds complicated, but it's really pretty basic. You probably do it every time you speak.
Think of the difference between the -o sound in the do of "How do you do?" and that of the last word in "How are you doing?" The last word of that sentence might be written *diwin if it were spelled phonetically the way the average modern American pronounces it. When that -o- shifts up to an -i-, that's i-mutation.
Say the vowels slowly, in order, out loud, shifting from one to the other without pause — "A-E-I-O-U" — and feel how they "happen" in different parts of your mouth. Philologists talk of "high" and "low," "front" and back." "A" is the lowest, "backest" of our vowels, and that's why doctors tell you to make that sound when they want to look down your open throat.
I-mutation is caused by the very human habit of laziness: taking the shortest distance between two points. The plural of man in ancient West Germanic, the ancestor of Old English, used to be a word something like *manniz. The speakers "cheated" on the first vowel in the word to be in position for the second vowel. It's the same thing you do with doing. It doesn't change the meaning of the word to do so.
So after hundreds of years of this, the plural came out as *menniz, or something similar, when people said it. Eventually, the shifted vowel itself comes to stand for the plural, and since laziness dislikes doing the same job twice, the syllable at the end of the word slowly shriveled and dropped off.
Most such suffix vowels were gone by the Old English period, but their effects remained and in a few cases still do. Some of the main places you can still find evidence of i-mutation are:
1. Abstract nouns formed from adjectives by adding -ith: foul-filth, hale-health, long-length, slow-sloth, strong-strength, wide-width, deep-depth.
2. Verbs formed from noun or adjective roots by adding -jan: doom-deem, food-feed, tale-tell, full-fill, blood-bleed, hale-heal.
3. Causative verbs formed from preterites of strong verbs by adding -jan: drank-drench, lie-lay, rose-raise, sat-set, drove-drive. Fell-fell is also an example, though it's not so obvious now.
4. Noun plurals in -iz: man-men, foot-feet, tooth-teeth, goose-geese, louse-lice, mouse-mice. Along with woman-women (derived from wif-man) these are the only survivors of this class, which was numerous in Old English and included such words as the ancestors of modern book, goat, and friend, which now have gone over to the -s plural.
5. Comparatives in -ir: old-elder, late-latter.
6. I-mutation turns up in an adjective formed from a noun by adding -ish in at least one important case: English (Old English Englisc) from the people called Angles.