The i and p mean that the package is either installed or is a package that's available to be installed.
For example
$ aptitude search aptitude
i aptitude - terminal-based package manager
p aptitude:i386 - terminal-based package manager
i A aptitude-common - architecture indepedent files for the aptitude package manager
p aptitude-dbg - Debug symbols for the aptitude package manager
p aptitude-dbg:i386 - Debug symbols for the aptitude package manager
v aptitude-doc -
man page
From man aptitude:
Unless you pass the -F option, the output of aptitude search will look
something like this:
output
i apt - Advanced front-end for dpkg
pi apt-build - frontend to apt to build, optimize and in
cp apt-file - APT package searching utility -- command-
ihA raptor-utils - Raptor RDF Parser utilities
description
Each search result is listed on a separate line. The first character
of each line indicates the current state of the package: the most
common states are p, meaning that no trace of the package exists on
the system, c, meaning that the package was deleted but its
configuration files remain on the system, i, meaning that the package
is installed, and v, meaning that the package is virtual. The second
character indicates the stored action (if any; otherwise a blank space
is displayed) to be performed on the package, with the most common
actions being i, meaning that the package will be installed, d,
meaning that the package will be deleted, and p, meaning that the
package and its configuration files will be removed. If the third
character is A, the package was automatically installed.
References