Profit vs Purchasing Power: What's the Real Deal?

Does a rise in price of what you invested mean you're only making money or actually losing purchasing power? I’ve been thinking about this. Like, is the point of investing just to score more dollars by putting in less? Or should we be focused on keeping our investments valuable over time? I hear a lot of people say they bought something for this amount and then, after a decade, sold it for that amount. But is that profit? I mean, with inflation eating away at fiat currency, how much of it is actually real profit?