The transition from brutal slavery and deep impurity to a sacred covenant with God is likened to a young bride being prepared for her wedding. The physical acts of bathing and anointing with oil serve as a profound correction to her earlier abandonment. In her infancy, she was left unwashed and utterly neglected, but now she is carefully readied for the wedding canopy [מלבי״ם].
The initial bathing cleanses away accumulated dirt and impurity [מצודת ציון, מצודת דוד]. On a symbolic level, this cleansing represents the redemption from Egyptian bondage and the emergence into freedom [רש״י]. The primary approach among commentators connects this to the moment just before the giving of the Torah at Mount Sinai. The Israelites were commanded to wash their garments and sanctify themselves, much like a newly freed slave who bathes and changes his clothes to wash away the impurity of his former surroundings [רד״ק, מצודת דוד, אברבנאל]. Others view this cleansing as the crossing of the Red Sea, an event that washed away the false beliefs of the people [מלבי״ם], or as a spiritual purification from the filth of idolatry [אברבנאל]. Alternatively, the water serves as a metaphor for the Written Torah, which is as universally essential to human life as physical water is to all living creatures [אדרת אליהו].
Following the initial bath, a deeper rinsing takes place to wash away the blood of birth or impurity [מצודת דוד, אברבנאל]. In the broader story of the nation, this rinsing signifies the removal of the grime left by the crushing physical labor of Egypt [רד״ק]. It also marks the end of the spiritual contamination that had clung to the people until it was completely removed at Mount Sinai [אדרת אליהו]. A Midrashic perspective suggests that this blood hints at the specific merits that protected the Israelites during the Exodus, namely the blood of the Passover sacrifice and the blood of the covenant of circumcision [אברבנאל].
Finally, the preparation concludes with the application of anointing oil [רש״י, מצודת ציון]. The purpose of this oil is to soothe and soften the flesh [מלבי״ם], particularly skin that had grown hard and calloused from years of grueling labor with mortar and bricks in Egypt. This softening reflects the physical rest, relief, and steady provision of needs that God granted the Israelites as they journeyed through the wilderness [רד״ק]. Spiritually, the oil represents the sacred anointing oil, or the foundational laws and statutes that were first given to the nation [מלבי״ם, אברבנאל]. From another perspective, if water represents the universally accessible Written Torah, the oil represents the Oral Torah. It acts as an added layer of intellectual and spiritual refinement, a deeper pursuit that not everyone engages in to the same degree [אדרת אליהו].