Do you have a local bike shop (frequently "LBS" on these boards) near you? If so, I'd recommend going in there on either a cold and dreary weekend day (should be some coming up), or in the middle of a week day, when the shop is not likely to be crowded. You want to go in at a time when the shopworkers can spend some time with you and chat a bit without anyone feeling too stressed or frazzled.

Go in there and explain to the salesperson just what you said in your first post, i.e., that you've been doing and enjoying a fair bit of riding on a relatively low-end bike, that there's no way you're going to be buying a new bike that very day, but that there's a pretty good chance that you might be fairly soon if you become convinced it's worthwhile.

A good salesperson in a good shop on a day that's not busy should be delighted to show you what they've got, to chat with you about what you've got and what the improvements would be, (you might consider taking your current bike in to show them), and to set up several models for short test rides around the shop. A bad salesman in a bad shop may belittle your current rig or try to hardsell you into buying something you're not ready for. It's perfectly OK to politely leave a shop like that, or at least to come back on a different day in hopes of finding a different salesperson if your shop options are limited.

Assuming you find a decent shopworker to talk to and that you can test ride a few bikes, note for yourself the differences between your current rig and what they're offering. The new bike may feel lighter and more responsive. Work the brakes. The new ones may be more powerful, stopping the bike quicker, more quietly, and more securely. Work through all the gears; try to ride some gentle hills around the shop if possible. You may find the better bike's gears shift quicker and more precisely. You may find a bike that fits your body better, or that for whatever reason just speaks to you in some way that tells you you've got to have it.

Or you may find that your current bike is just fine for what you want to do, and that you don't see any compelling reason to dump cash into a new one. That's fine too. It's your ride and you can get a good workout, get fit, or commute on any bike that's safe, reliable, and fun enough that you won't leave it sitting at home in the garage.

As you continue to ride you'll probably see more and more the advantages to higher quality mounts, but if you're enjoying what you've got you're right to believe that there's no reason to rush into something you don't understand.