Grimm's Law is considered a product of the wildly veering mind of Jacob Grimm (philologist, anthologist, and nationalist), though it appears as if a lot of the heavy lifting may have been done by the Dane Rasmus Rask. Then there's Verner's Law; I'm hoping somebody writes about that one soon. ¹

Grimm's Law is an observation of sound shift patterns over time (and in the course of loan-word assimilation) in Germanic Languages: 't' mutates into "th", which in turn becomes 'd', which ultimately returns to 't'. This will be familiar to those who have heard Americans from Pennsylvania and New Jersey speak of "a hundrit" this, or "I wantit that". Me "brudder" wanted that too, hm? I appeal also to those Anglophones who have gingerly and fearfully speculated about the meaning of "blutwurst".

Other common changes include:

• 'v' to 'f', as in the German "vater" becoming the English "father". We also get a 't' to "th" shift there at no extra charge save for shipping and handling. The Latin "pater" seems relevant.
  
  We should also note the long-obsolete habit of replacing a terminal 'f' with a 'v' when adding additional syllables to a word, as in "thief" to "thieves", "calf" to "calves", "dwarf" to "dwarves", and the glorious "beef" to "beeves" (I kid you not!). Perhaps in some way related, an unvoiced "th" becomes voiced in the same way: "Wreath" to "wreathes"; "scythe" to "scythes".
  
  
• 'p' to 'f' to 'b' and back to 'p': "Labial", "lip"; "pedal", "foot"
  
  
• 'k' to 'h' to 'g': "Genual", "knee"; etc.

My book here sez dat alla dese sequences move from unvoiced stop to unvoiced continuant to voiced stop. I'm willing to take that on faith until I figure out what the hell it means.

CentrX observes that Grimm's name is often spelled "Jakob"; my source had a 'c', but I've found an equal number of references to each on the net, so it seems like a toss-up.

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¹ When first I wrote this writeup, I hadn't spotted any linguists running around loose here. Since that time, we've gotten one or two, and I'm not going to write any more about stuff I'm so ill-qualified to discuss if competent authority is in the house.

The first stage of Grimm's Law is the Germanic consonant shift, whereby these Proto-Indo-European phonemes changed their values:

    Indo-European       Germanic
    =============       ========
     p   b   bh         f  p  b
     t   d   dh    -->  th t  d
     k   g   gh         h  k  g
     kw  gw  ghw        hw kw gw

So, for example, PIE *pod- becomes *fot- in Germanic (ending up eventually as 'foot' in English). To compare to another language, *bher- in Greek produces 'pherein' ("to carry") and *beran in Germanic (becoming 'to bear' in English).

The second stage in Grimm's Law is the High German consonant shift, which applies (aptly) to High German, and also apparently appeared in the East Germanic language Lombardic. It changed p, t, and k to (p)f, (t)s, and (k)h. (I'd give the full changes but I can't find them right now.)

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FYI, the Jakob/Jacob Grimm in Grimm's Law is one of the Brothers Grimm, the very same Grimm as in Grimm's Fairy Tales.