The potential uses of brain clones is highly speculative, since we still don't have the computing power to create one. Here are some of the ideas that have been suggested.
Exploring Mars
Preserve a Departed Mentor
Interactive History
A brain clone could tell your stories and answer questions about your life. Because it is interactive, it is better than an autobiography.
Trust Advisor/Administrator
Trusts can last forever, but instructions governing them quickly become dated. A brain clone may be the best way to assure that your wishes and directions adapt to changing times and circumstances.
Ongoing Influence
You can only really continue to be an ongoing influence if part of you never goes away.