You can use
apt-cache search. For example to search firefox:
apt-cache search firefox
This is the according snippet from
man 8 apt-cache:
search regex [ regex ... ]
search performs a full text search on all available package lists
for the POSIX regex pattern given, see regex(7). It searches the
package names and the descriptions for an occurrence of the regular
expression and prints out the package name and the short description,
including virtual package names. If --full is given then output
identical to show is produced for each matched package, and if
--names-only is given then the long description is not searched,
only the package name is.
Separate arguments can be used to specify multiple search patterns
that are and'ed together.