dpkg --status (shortened as dpkg -s) shows a package's status (which is recorded in /var/lib/dpkg/status).
The status consists various details:
$ dpkg -s fonts-open-sans
Package: fonts-open-sans
Status: install ok installed
Priority: optional
Section: fonts
Installed-Size: 2822
Maintainer: Debian Fonts Task Force <pkg-fonts-devel@lists.alioth.debian.org>
Architecture: all
Multi-Arch: foreign
Version: 1.11-1.1
Description: humanist sans serif typeface by Steve Matteson
Open Sans is a clean and modern sans-serif typeface designed
by Steve Matteson and commissioned by Google.
…
dpkg -s can be used to verify if a package is installed:
$ Debian ~ dpkg -s no-such-package
dpkg-query: package 'no-such-package' is not installed and no information is available
Use dpkg --info (= dpkg-deb --info) to examine archive files.