Step 1: What oxidation of an alcohol requires.
Oxidation converts an alcohol to a carbonyl compound by removing the $-OH$ proton and one alpha-hydrogen (the hydrogen on the carbon bonded to $-OH$) to form a $C=O$ double bond.
Step 2: Structure of a tertiary alcohol.
In a tertiary alcohol ($R_3C-OH$), the carbinol carbon is bonded to three alkyl groups and carries no hydrogen atom; there is no alpha-hydrogen available for removal.
Step 3: Why forming $C=O$ is impossible.
Without an alpha-hydrogen, a $C=O$ bond cannot form unless a C-C bond is broken. Common oxidizing agents such as acidified $K_2Cr_2O_7$ do not supply enough energy for C-C cleavage.
Step 4: Conclusion.
Therefore, tertiary alcohols remain unaffected by ordinary oxidizing agents and are resistant to oxidation.