The intention (niyyah) means resolving to fast. It is essential to have the intention the night before, night by night, in Ramadaan.
(Fataawa al-Lajnah al-Daa'imah, vol. 10, p. 246)
Some scholars were of the view that in the case of a repeated act of worship, it is sufficient to form the intention once the first time one does, unless the sequence of repetition is interrupted, in which case a new intention must be formed. On this basis, if a person has the intention of fasting on the first day of Ramadaan that he will fast this whole month, that is enough to cover the whole month, so long as he does not have an excuse to break his fast and thus break this continuity, such as traveling during Ramadaan. In that case, when he wants to resume fasting he must form the intention of fasting again.
This is the more correct opinion, because all the Muslims, if you ask them, will say that they intend to fast the whole month from beginning to end. So even if the intention is not formed literally, it is there by implication, because the basic principle is that it does not stop. Hence we say that if the continuity is broken for some permissible reason, then one starts fasting again, the intention must be renewed. This is the view which brings peace of mind.
Reproduced from Islam QA