Glad that you read this. It's a bit technical but I'll try to explain.
Every account on Hive Blockchain has two influence/authority stats: "Reputation" & "Hive Power."
Rep (Reputation) refers to how your content/posts/comments are seen by other users. It increases when you get Upvotes & decreases with Downvotes. Some interfaces like Ecency won't show your posts and comments at all if your Rep is low. (You can see it beside your user name: Your current Rep is 46.)
HP (Hive Power) is how much "shares" you have in the ecosystem. If you have %1 of all HP, it's like owning %1 of the community. HP decides many things, like how much your upvote is worth. How many resources you can use from the system per day. (With 1 HP you can only post/comment once per day.) HP also tells people outside of the blockchain how much people invested in it, making the currency #HIVE more valuable.
The thing is, HP can be turned into normal (we call it liquid) Hive currency & vice-versa. When you Power UP, you put your HIVE into HP. When you Power Down, you turn your HP into HIVE, but powering down takes a while to prevent the abuse of the system. (Last time I checked it was 13 weeks, but some leaders want to change that into 4 weeks.)
That's why Powering UP is a big deal in this website, because you're telling the system that you don't want to use your money outside of it, but for things inside of it (like Upvoting) which makes the system more valuable.
I hope I explained easily, if you didn't understand now, you can go back when you familiarize yourself with HIVE more.