I'm no expert but this is what I understand. A disorder is something which generically breaks some invariance of the Hamiltonian or some deviation from the lattice periodicity. When some disorder is present, all points in the lattice are not equivalent. For example, consider the tight-binding model $$H=\sum\limits_{i}\epsilon_0|i\rangle\langle i|+\sum\limits_{i,j}(h_{ij}|i\rangle\langle j|+|j\rangle\langle i|)$$ where $\epsilon_0$ is called the on-site energy and $h_{ij}$ is called the hopping parameter. If $h_{ij}=h\delta_{i+1,j}$, then it does not model a disorder. However, if $h_{ij}$ is different for different $i,j$, it models a *static disorder* and breaks the discrete translation symmetry of $H$. Physically it corresponds to sprinkling some ${\rm Ni}$ atoms in a crystal of ${\rm Cu}$ atoms. Also by making $h$ to be a random function of time $h(t)$ i.e., a stochastic variable one can introduce a *dynamic disorder*.