When Grimm's law was discovered, a strange irregularity was spotted in its operation. The Proto-Indo-European (PIE) voiceless stops *p, *t and *k should have changed into Proto-Germanic (PGmc) *f, *ş (dental fricative) and *x (velar fricative), according to Grimm's Law. Indeed, that was known to be the usual development. However, there appeared to be a large set of words in which the agreement of Latin, Greek, Sanskrit, Baltic, Slavic etc. guaranteed PIE *p, *t or *k, and yet the Germanic reflex was a voiced consonant (*b, *d or *g).
At first, irregularities did not give scholars sleepless nights as long as there were many examples of the regular outcome. Increasingly, however, it became the ambition of linguists to formulate general and exceptionless rules of sound change that would account for all the data (or as close to the ideal as possible), not merely for a well-behaved subset of it.
One classic example of PIE *t > PGmc *d is the word for 'father', PIE *pH2te:r (here *H2 stands for a laryngeal, and the colon marks vowel length) > PGmc *fade:r (instead of expected *faşe:r). Curiously, the structurally similar family term *bhra:te:r 'brother' developed as predicted by Grimm?s Law (Gmc. *bro:şe:r). Even more curiously, we often find both *ş and *d as reflexes of PIE *t in different forms of one and the same root, e.g. *werş- 'turn', preterite *warş 'he turned', but e.g. preterite plural and past participle *wurd- (plus appropriate inflections).
Karl Verner was the first scholar who put his finger on the factor governing the distribution of the two outcomes. He observed that the apparently unexpected voicing of voiceless fricatives (and their falling together with *b, *d, *g) occurred if they were non-initial and immediately preceded by a syllable that carried no stress in PIE. The original location of stress was often retained in Greek and early Sanskrit, though in Germanic stress eventually became fixed on the initial (root) syllable of all words. The crucial diference between *pH2te:r and *bhra:te:r was therefore one of second-syllable versus first-syllable stress (cf. Sanskrit pitá: versus bhrá:ta:).
The *werT- | *wurd- contrast is likewise explained as due to stress on the root versus stress on the inflectional suffix (leaving the first syllable unstressed). There are also other Vernerian alternations such as illustrated by Modern German ziehen | (ge)zogen 'draw' < PGmc. *tiux- | *tug- < PIE *déuk- | *duk- 'lead'.
There is a spinoff from Verner's Law: the rule accounts also for PGmc *z as the development of PIE *s in some words. Since this *z changed to *r in the Scandinavian languages and in West Germanic (German, Dutch, English, Frisian), Verner's Law resulted in the alternation /s/ versus /r/ in some inflectional paradigms. For example, the Old English verb ceosan 'choose' had the past plural form curon and the past participle (ge)coren < *kius- | *kuz- < *g^éus- | *g^us- 'taste, try'. We would have coren for chosen in Modern English if the consonantal shell of choose and chose had not been generalised. But Vernerian /r/ has not been levelled out in were < PGmc. *we:z-, related to was. Similarly, lose, though it has the weak form lost, also has the compound form forlorn.
It is worth noting that the Verner's Law comes chronologically after Grimm's Law (because Grimm's Law provides most of its input) and before the Germanic shift of stress to the initial syllable (because the voicing is conditioned by the old location of stress). The stress shift erased the conditioning environment and made the Vernerian variation between voiceless fricatives and their voiced alternants look mysteriously haphazard.
The moral of Verner's Law is that crucial evidence necessary to sort out the historical evolution of a linguistic lineage may reside where few people would dream of looking for it. Verner found it "out there" in Greek and Sanskrit, while everyone else had tacitly assumed that Germanic changes can be explained in Germanic terms without recourse to external comparison.