Here's how it evolved:
* Latin: *alter* (meaning "other")
* Old French: *alter* (meaning "other, different")
* Middle English: *alter* (meaning "to change, to make different")
* Modern English: *alter* (meaning "to change, to make different")
So, when we talk about "altering" something, we are essentially talking about making it "other" or "different" from what it was before.