أَعُوذُ expresses the reader's seeking protection, بِاللّٰهِ identifies Allah as the One whose refuge is sought, and مِنَ الشَّيْطَانِ الرَّجِيمِ specifies the danger from which protection is requested.
أَعُوذُ بِاللّٰهِ
I seek refuge in Allah.
Breaking down the meaning helps comprehension, but the complete formula must still be recited with correct vocalization. In particular, ع and ذ should not be replaced by familiar but different sounds; their articulation will be studied in later lessons.