High blood pressure (hypertension) has been found in 10-23% of cats with hyperthyroidism. (Taylor et al, 2017) It has also been shown that nearly 25% of cats with normal blood pressure at the time of diagnosis go on to develop high blood pressure once their condition is under control (Taylor et al, 2017). The reason why this occurs is poorly understood but explains why your vet might suggest blood pressure monitoring as part of their care.
Without intervention, high blood pressure can cause bleeding in the retina (back of the eye) or retinal detachment. This can lead to sudden blindness. High blood pressure can also cause damage to the blood vessels in the kidneys and put extra pressure on the heart, leading to problems here too.