Aptsh is a pseudo-shell for systems with Apt package managing tool. It's similar to AptShell from AptRpm, but it works not only with AptRpm (actually, it's being developed with Debian's Apt). Also, it's inspired by The Poldek from PLD.
But, what does it exactly do? Well, if you use Apt, you should know the situation - search for a package with apt-cache and copy its name to apt-get, repeat. And, you probably do not enjoy the situation before last execution of apt-get. If so, consider using aptsh - it offers that cute TAB completion which you always use while unix-shelling. It's smart enough to decide whether you're trying to remove or install/upgrade a package, and doesn't suggests you to remove your Gnome since you are a KDE maniac who has never seen (and never installed) that ugly Gnome. In short: a tool which makes life easier, although it's not necessary.
You may find few similarities between Aptsh and things like Wajig or Feta. Yes, it's the same sort of applications.