What model do you own and what's the current firmware version its currently running?
As for the benefits of jailbreaking: installing applications that Apple would never approve of like phone UI and system tweaks, which improves upon the OS a lot, and of course 
improves how?
I only have a few apps/tweaks installed, basically the ones I use on daily basis, but they should give you an idea:
- Lockinfo: replaces the lockscreen with neat and organized lists of calender events/missed called/unread mail or messages/unchecked push messages/ weather forcast. It can also be set as your homescreen and/or linked to a touch gesture that activates it as a drop down layer. Customizable and themeable.
- BiteSMS: powerful SMS app, has many features. I mainly use it for the quick reply/compose feature (compose and reply anywhere, eliminating the need to exit apps in order to use those features).
- Action menu: adds to the copy/paste pop-menu extra functions like lookup (search/dictionary/translate), scroll up/down, add location, clipboard history, favorites.
- Fullscreen Safari: self explanatory.
- Safari Download Manager: self explanatory.
- iFile: think of it as a windows explorer or Finder for the iOS. Can view a wide variety of files, even zip and unzip archives.
- infinifolders: Add as many apps to any folder as you like, unrestricted by the 12 apps per folder limit set by apple.
- Folders within folders: self explanatory.
- infinidock: have as many icons as you like on your dock, set them either to scroll infinitely or be spread among several pages.
- remove background: simple tweak that removes all backgrounded apps by holding the status bar.
- sbsettings: swipe the status bar anywhere to reveal a drop down menu containing a variety of toggles (wifi/3G/bluetooth/brightness...etc), saves you the trouble of going to the Settings menu to toggle any of them on/off. Customizable and themeable.
- Screendimmer: you can set a timer to dim the screen/turn it off so you don't have to rely on the annoying auto-lock feature in order to preserve the battery.
- switcher mod: all icons on the switcher dock have visible (x) so you don't have to hold an icon, wait for the to wiggle effect, then start closing them off. Has more features that I don't care for/recall.
- Yourtube: save youtube videos.
- Winterboard: Themes management app.
- WiFi Sync: sync with iTunes over wifi.
- Pwntunes: skip the iTunes altogether and drag and drop your files directly to your iDevice.
I used to have a lot more before updating, I'm waiting for most of them to receive compatibly updates.
Edit: I think I met my applefaggotry monthly quota in less than 5 posts.