If an implementation isn't constant time it can potentially leak information about the key. i.e. the relative length of time it takes to encrypt may be depende

If an implementation isn't constant time it can potentially leak information about the key. i.e. the relative length of time it takes to encrypt may be dependent on properties of the key. So an attacker that can measure how long it takes you to encrypt something can begin to derive the key. Similar attacks occur when your encryption uses lookup tables depending on key bits, uses different amounts of power, etc. It's a surprisingly effective attack surface, and why the industry is moving away from older style schemes like AES and towards ARX based constructions like ChaCha.