After the اِسْتِعاذَة wherein we proclaim that we have taken refuge in Allah, as we want to distance ourselves from the evil, we move onto the بَسمَلة basmalah - the saying of بسم الله الرحمن الرحيم, in which we are seeking to attract the good.
The first part of it, بسم الله, is normally translated as ‘With the name of Allah’. It is clear that this phrase holds no meaning by itself, but rather it must be attributed to an action, “With the name of Allah I am waking up]”, “With the name of Allah I am eating this food”, “With the name of Allah I am slaughtering this animal” and so on. The absence of a mentioned action means that it is open-ended and can - and does - apply to any action we are performing.
The prefix "بـِ" at the beginning of the word "بسم" carries multiple meanings within the phrase. It signifies that the action is undertaken with the remembrance of Allah and prioritizes Him above everything else, highlighting the sincerity with which the action is performed. Moreover, it acknowledges our reliance on Allah for every deed, understanding that without His presence, our actions lack blessings. Lastly, it expresses our need for Allah to accept our deeds.
So when we say بسم الله we are essentially saying, "O Allah, I begin this action in Your name, keeping You in my thoughts and prioritizing You above everything else. I seek Your blessings in this endeavor, and I implore You to accept it from me.”