In a healthy mental state; sane and rational. For example,
No one in his right mind would ski down this icy slope. This expression is often used in a negative construction, as in the example. The positive sense appears in the New Testament (Mark 5:15), where a deranged man whom Jesus helped is now "sitting, and clothed, and in his right mind." The antonym
out of one's mind, as in
You must be out of your mind to swim in that icy stream, is from the same period. [c. 1600] Also see
go out of one's mind.