If you’re traveling to Iran during Ramadan you should be aware of and sensitive to the fact that the people are fasting:

1) In some Muslim countries just like Iran, it is illegal to eat and drink in public at daylight during Ramadan, so check before you go. In any case, it's more respectful to avoid eating, drinking or smoking in public. The people would appreciate the fact you are showing respect and awareness.
2) Business hours may be shortened during the day throughout Ramadan so check if you need to use the bank, shops or other services.
3) Some restaurants are closed or operated different opening hours during Ramadan, while the more tourist-oriented restaurants are usually remained open as usual. 
4) In the evening, 'Iftar' is the time when the fast is broken and families and friends get together to eat a meal. It can be a busy time on the roads, so if you can avoid using transport around this time it will make things easier for you.
5) Towards the end of Ramadan, people traditionally visit relatives to celebrate Eid (or Eid al-Fitr), national holiday at the end of Ramadan. As a result, the roads and transport can also be very busy at this time, so book ahead if you want to travel then.