cyclical is generally used in conjunction with the business cycle. eg. cyclical unemployment would happen whilst the business cycle is in a downturn phase (recession)
whereas structural is more related to skills within the labour market. even when in an upturn period of the business cycle there can still be unemployment because the skills of those unemployed dont match the jobs available.
structural unemployment is because the skills of the unemployed dont match the jobs available (as already stated). this is because the economy is undergoing some sort of structural change where certain skills become useless and cause unemployment.
for example, person A that was really good at repairing a VCR or discman (or some other product not used anymore) would find himself structurally unemployed because his skills at repairing are no longer needed. people use VCR's and discmans much less these days and use dvd players and ipods in thier place.
so now person A is unemployed because no one wants his services while there are now jobs available in fixing dvd players and ipods instead of older equipment. hence person A now has jobs that dont match the jobs available.
structural unemployment directly related to structural change in the economy which is why all of these changes occur