Dizziness is a common symptom during pregnancy and is mainly caused by insufficient blood supply to the brain. Some may feel instable when standing or walking, some may feel black scene or even suddenly syncope. Usually dizziness in pregnancy isn't a big problem, eating more foods rich in iron or take iron supplement will help relieve the symptom. However, if the dizziness is caused by severe anemia, or hypertension, it's a different story.
We'd recommend you to go visit your Obstetricians regularly, tell him/her about your feeling, have your blood pressure, heart rate and blood panel tested.