Peace be upon you. The intention in acts of worship generally means having the purpose of performing the act as a means of drawing closer to Allah. In other words, you should know that you are praying, for example, the Fajr prayer, and you are doing it for the sake of Allah. If asked what you are doing, you would respond, 'I am praying the Fajr prayer.' It is not required to verbally express this intention either in your heart or on your tongue. Therefore, simply standing up to perform the Fajr prayer with the intention of drawing closer to Allah is what is meant by intention.
Source:
Ayatollah Khamenei: Easy Jurisprudential Rulings.
Ayatollah Sistani: Official website + Selected Issues, Rulings on Prayer: Parts of Prayer and Its Obligations, Intention.
May you be successful in all good.