Internal conflict refers to the psychological conflict within a character; this internal conflict usually stems from opposing emotions, goals, or desires. External conflict refers to the often physical or action-oriented conflict a character engages in; here, the character is basically confronting enemies who stand in the way of his/her goals.
In The Call Of The Wild, we see manifestations of both internal and external conflict as manufactured by the Law Of The Club And The Fang (incidentally, also the title of the second chapter). In Chapter One, Buck gets his first taste of the law of the Club. That's when the man in the red sweater first introduces Buck to the ' reign of primitive law.' Buck learns that a man with a club will always call the shots:
...a man with a club was a lawgiver, master to be obeyed, though not necessarily conciliated.
Now, the word 'conciliated' is very important here. 'Conciliate' simply means 'to make peace with.' Buck decides that he doesn't want to condescend to servile submission, nor does he wish to share the fate of another dog who would 'neither conciliate nor obey, finally killed in the struggle for mastery.' So, Buck's internal conflict is between choosing whether to conciliate, obey, or to do both in his struggle to survive under the Law of The Club. He decides (internal conflict) that he will outwardly submit in the external conflict with a man who wields a club but stubbornly refuses to make peace with any master who resorts to such violence to gain his respect.
On to the Law of the Fang. In Chapter Two, Buck witnesses the horrible death of the good-natured Newfoundland, Curly. When Curly tries to make friends with a Husky, she is ferociously attacked and torn apart by about thirty to forty Huskies.
This is Buck's introduction to the Law of The Fang: the fiercest and strongest survive; the weak are torn limb from limb. Buck learns that once a dog is down, he will never get up again. He resolves never to let that happen to him. The internal conflict is when Buck determines how to survive within the confines of the Law of The Fang; in the end, he decides to bide his time to wait for the best possible moment to take down the greatest threat, Spitz, in order to cement his position as head Husky. The physical conflict between Spitz and Buck is the external conflict.
This physical, external conflict for preeminence under the Law Of The Fang is described in the third chapter 'The Dominant Primordial Beast.' Buck bides his time until he is confident that he is Spitz's equal in 'strength, savagery, and cunning.' The final battle between Spitz and Buck results in victory for Buck, his ferocity, cunning, and imagination the hallmark of a fearless, primordial beast.