Double-entry refers to the number of accounts related to a transaction, rather than the process of entering it twice.
When you think about it, all transactions have naturally (at least) a from and a to account. In the simplest example, I move $100 from one checking account to another. This is a pain to model in a spreadsheet, where I literally create two entries, but very easy to model in an electronic dual-entry system where I create a single transaction with a from and a to end point, and an amount.
Consider if I decide to buy a stock from my checking account. The from is my checking account, and then there are two "to" accounts - an account which models the value of the stock, and an account for the vendor's charges for the purchase. I might decide to aggregate all such bank charges to a single virtual account for this purpose. In this case, that virtual account would be the same as a "category" in a spreadsheet based model.
It can also make budgeting and cash-flow visualization easier. I have a virtual account called "Holiday Budget", which makes a transaction to another virtual account called "Spent on Holidays" of $x every month. Whenever I spend money on a holiday item from my checking account, the "from" is my checking account, and the "to" is my "Holiday Budget". This keeps my net-worth and budgeting reports very simple - they say I spend the same $x on holidays every month - while accounting for some very lumpy spending. I can easily see if I'm over or under budget by looking at the value of the virtual account "Holiday Budget" at any point.
It makes recording the value of unconventional assets easier. When I buy a laptop, I create a new account for the laptop, and transfer the money from my checking account to the virtual account that represents the value of the laptop. Every month, I draw down money from the laptop account in to an account called "depreciation". This helps me keep my budget reports insulated from lumpy spending too.
A big use-case as well for me is the purchase of expensive refundable plane tickets - essentially, I buy personal futures in plane tickets when I see a good price. The virtual accounts that dual-entry allows means that when I buy a refundable ticket, I treat it as an asset in a virtual account until it's used. Again, this helps me track my spending and budgetting more effectively.