HTTPS does three interrelated things:
Encryption - the data cannot be read by an intermediary, which protects your readers' privacy. You don't want people to know what pages you read on BigBank.com or EmbarassingFetish.com.
Tamper Proofing - the data cannot be changed by an intermediary, which protects your readers' (and your server) from someone messing with the data, say substituting one bank account number for another when setting up a payment, etc.
Site Authentication - ensures that the browser is connected to the server it says it is, which also prevents proxying. Without this an intermediary can impersonate any site.
Before the big push for encrypting everything it was not uncommon to hear of ISPs inspecting all traffic to sell to advertisers, or even injecting ads directly into pages. HTTPS makes this much more difficult.