Accent, on its own, refers to the amount of emphasis or stress we apply to certain syllables and words. Consonant shift, again on its own, pertains to the way the pronunciation of consonants changes throughout the history of a language or dialect.
Both of these terms, however, have their own places in Grimm's Law and Verner's Law. Grimm's Law depicts correlations between Germanic and Indo-European languages, as described in Jacob Grimm's "Germanic Grammar." It was a breakthrough for linguists who had previously thought that consonant shift only affected certain words instead of being something natural that happens to a language.
The law itself discusses two consonant shifts affecting different languages at different points in time: one affecting Indo-European consonants and another affecting mainly Germanic ones. Those shifts are the ones that affect, for example, how f, th, and h sounds are pronounced in English languages—making the English "fod" sound similar to the Greek "pod" because of the shift from p, t, and k sounds.
Verner's Law incorporates accent and is studied in connection to Grimm's Law, as it explains the exceptions to the rule. The changes in accent (or emphasis) are what cause the consonant shifts Grimm discussed; however, Verner saw that Grimm's Law was only valid when the accents fell onto certain syllables. English's f, th, and h sounds only mirrored the p, t, and k of Indo-European languages when falling onto certain root syllables. Falling on any other syllable, the f, th, and h sounds begin to mimic equivalents of other languages.