A chemical specie will always exist in equilibrium with other forms of itself. The other forms may exist in undetectable amounts but they are always present. These other forms arise due to the natural disorder of nature that we call entropy (it's impossible to be perfect). As an example, pure water consists of the molecular compound and dissociated ions that exist together in equilibrium:
H2O(l) H+(aq) + OH-(aq)
The (l) subscript refers to the liquid state, and the (aq) subscript refers to ions in aqueous solution. Pure water at room temperature contains 1x10-7 M H+ and OH-
The same is true for chemical reactions. The reactants will always exist in equilibrium with the products of the reaction. The reactants or products might exist in undetectable amounts, but they are always present.
At equilibrium the partial pressures or concentrations of the reactants and products are no longer changing, that is they have reached a steady state. An important point to remember though is that on the molecular level reactant molecules (or atoms or ions) are still forming products, and product molecules are returning to reactants. At equilibrium, the rate at which reactants go to products is equal to the reverse reaction of products going to reactants.