The simplest way to distinguish among solids and liquids is to look at their microscopic structure.
Solids have an extrimely high ordered spatial disposition of their molecules. Knowing distances and orientation of few neighboring molecules in a solid gives us information about all the other molecules composing it. Knowledge of the local geometry can be transferred to the all solid. In a solid the molecules sit in fixed locations forming a rigid structure. They cannot freely move out of those sites. Molecules in solids are equidistant one from another and they all have the same orientation.

Microscopic structure of a crystalline solid

In liquids the situation changes drastically. The molecules do not show any kind of ordered spatial disposition. They are randomly oriented and the distance as well as the number of neighboring molecules changes. There is not a rigid structure they can fit in and the molecules can freely flow around. Knowledge of the local geometry cannot be transferred to the whole fluid.

Microscopic structure of a liquid

The regularity in the distances between the molecules is called positional order while the regularity in their orientation is called orientational order.
Liquid crystals lie in between. As in the liquids they are free to flow around and they do not have any global rigid structure (no positional order) but as solids the have a substantial orientational order. The rod-like molecules composing a liquid crystal have the ability to align themselves in some preferential axis usually called director. It is this ability which allows us to discriminate among solid, liquid-crystal and liquid phase. Liquid crystals molecules have a preferred direction along which they "like" to point but still is present some sort of weak disorder in their orientation.

Microscopic structure of a liquid crystal

In order to give a quantitative estimate of the level of order in a particular phase, is often useful to introduce a quantity called order-parameter. One of the possible expressions for it can be thought as follows:
let's denote with q the angle between the molecule long axis and the director. This quantity tells us how far from a perfect alignement that molecule is. In order to have a feeling for the whole material we have to add up all the angles of all molecules and perform an average of this value.

We define the order parameter as

m=1/2<3(cosq)²-1>.
In the liquid phase the molecules will be randomly oriented so q can get all possible values from 0-360 degree with the same probability, leading to the result m=0. In the solid phase all molecules will be aligned with the director. The angle for all of them will be 0 meaning m=1. For a liquid crystal tipical values of m variate from 0,3 to 0.9 depending on the particular temperature.