Some say reading in Greek and Hebrew versus reading in English is like the difference between watching a show in color versus black and white. Others might say something like 2D versus 3D. I don't think these are the best way to describe the experience. Reading in Greek and Hebrew slows me down and helps me rummage around in the text and reflect. For me, that's the core idea. It gives me something to do.
I'm asking and answering this question as someone who initially learned the languages to read and teach Scripture. I'm going to write more about other benefits and things that flow from this rummaging and slow down, but in this post I just want to lay the foundation. How many times have you sat down to prepare to teach or preach and you read your passage and think, "Ok, now what?" If you are reading in the original languages you have so many different resources and tools to explore, and I'm thinking primarily about lexicons and concordances. If you don't regularly read and work with the original languages, all you can do is skim the surface of an entry in BDAG or HALOT. Exploring contemporary literature, figures of speech, the metaphors used in your passage, looking at a words full range of meaning and determining which meaning is relevant for your passage — these are things you can actually engage in yourself if you can read the language.
But in my opinion, those things are not the primary benefit of the original language slow down. The real benefit comes in your day-to-day reading. It's about stripping away the familiarity of your natural language and lingering over the original words. Especially for the first few years of reading, you have to decipher every word and phrase, and the fog never really lifts. Sure, after a few years, you may be able to read one or two or four chapters in an hour, but it's still not English. You're moving slower, and when I do this, I find that I make connections with other portions of scripture that I wouldn't make otherwise. With certain phrases come flashes of other stories or scenes, and my imagination takes off. This sort of reading isn't about exegesis. It's about rummaging. It's about trying to step through the wardrobe into the real world of God's presence.