This reaction is an example of the dehydration of cyclic alcohols. The reaction proceeds in the following steps;
1) The first step of the process is the protonation of the cyclohexanol by the acid. This now yields H2O^+ attached to the cyclohexane ring.
2) the water molecule, which a good leaving group now leaves yielding a carbocation. This now leaves a cyclohexane carbocation which is highly reactive.
3) A water molecule now abstracts a proton from the carbon adjacent to the carbocation leading to the formation of cyclohexene and the regeneration of the acid catalyst. This is an E1 mechanism because it proceeds via a carbocation intermediate and not a concerted transition state, hence the answer.
