Definition
Definition (one dimensional): A function $f: \real \to \real$ is unimodal if there exists a point $m$ such that $f$ is monotonically increasing for $x \le m$ and monotonically decreasing for $x \ge m$.
Definition (multiple dimensions): A function $f: \real^d \to \real$ is unimodal if there exists a point $\m$ such that for all $\norm{\u}=1$, $f(\m + x\u)$ is a monotone decreasing function of $x$.
Properties
A unimodal function has exactly one strict local maximum; furthermore, this point is the global maximum.
Sufficient conditions
A sufficient (but not necessary) condition for unimodality is that $f$ is strictly concave and attains its maximum at some point $\m$. Along any ray $\m + x\u$ with $x \ge 0$, $f$ is then a strictly concave function of $x$ that is maximized at $x = 0$, and is therefore decreasing.
Concavity alone is not sufficient: a constant function is concave but has no unique mode, and a strictly concave function such as $\log x$ need not have a maximum at all.