Meaning : As the agent of or on someone's part (usually expressed as `on behalf of' rather than `in behalf of').
Example :
The guardian signed the contract on behalf of the minor child.
This letter is written on behalf of my client.
Meaning : For someone's benefit (usually expressed as `in behalf' rather than `on behalf' and usually with a possessive).
Example :
In your behalf.
Campaigning in his own behalf.
Spoke a good word in his friend's behalf.