Empirical cumulative distribution function: a step function increasing by $1/n$ at each unique $X$-value that occurred in the sample.
Consider a numeric or at least ordinal random variable $X$ and a random sample of size $n$ from the distribution of $X$, $x_{1}, x_{2}, \dots, x_{n}$. The ECDF $F_{n}(x)$ is a step function increasing by $\frac{1}{n}$ at each unique $X$-value that occurred in the data, when there are no ties. When $k$ values are tied at one value of $x$ the increment is $\frac{k}{n}$. The formal definition is $F_{n}(x) = \frac{1}{n}\sum_{i=1}^{n}I(x_{i} \leq x)$ where $I()$ is the indicator function. (For further explanation, see Integrating an empirical CDF. For a modified estimator of the CDF, visit PIT on a sample with m bins, and KS test used to estimate a good value for m.)
As construction of the ECDF requires no binning, the ECDF is unique and is often a good replacement for a histogram.
