Textpattern is free, open source software, distributed under the GNU General Public License Version 2.

Briefly, that means you can distribute Textpattern, in part or full, in its original form or with modifications and additions, provided you distribute it under the GPL. Distributing any part of Textpattern, including derived works, under any other license, is not permitted.

Textpattern may be used for any purpose, including commercial web sites. The license explicitly states that “the act of running the Program is not restricted” by the GPL.

The GNU project maintains a list of Frequently Asked Questions about the GPL.

Some that are likely to be of interest to Textpattern users:

Plugin licenses:

http://www.gnu.org/licenses/gpl-faq.html#GPLAndPlugins

Textpattern shares memory space, functions and data structures with plugins, which suggests plugins must be distributed under the GPL.

Integrating Textpattern with other proprietary software:

http://www.gnu.org/licenses/gpl-faq.html#GPLInProprietarySystem
http://www.gnu.org/licenses/gpl-faq.html#TOCMoneyGuzzlerInc
http://www.gnu.org/licenses/gpl-faq.html#GPLIncompatibleLibs

Linking or integrating Textpattern with proprietary software is at best problematic (limited to specific types of software interfaces, such as a fork/exec), at worst a breach of the license agreements of both software applications.

Private modifications:

The GPL doesn’t require users to make their own private modifications public:

http://www.gnu.org/licenses/gpl-faq.html#GPLRequireSourcePostedPublic
http://www.gnu.org/licenses/gpl-faq.html#UnreleasedMods

The GPL does not require you to release your modified version. You are free to make modifications and use them privately, without ever releasing them. This applies to organizations (including companies), too; an organization can make a modified version and use it internally without ever releasing it outside the organization.

Commercial distribution:

Providing a copy of Textpattern to someone outside your own company is considered distribution under the GPL. The GPL explicitly allows you to sell copies of Textpattern:

http://www.gnu.org/licenses/gpl-faq.html#DoesTheGPLAllowMoney

However, web developers or designers who distribute a copy of Textpattern (original or otherwise) to their clients, must do so under the GPL. You’re not required to provide a copy to anyone else, but you can’t prevent your client from copy or distributing it under the GPL if he chooses:

http://www.gnu.org/licenses/gpl-faq.html#InternalDistribution
http://www.gnu.org/licenses/gpl-faq.html#DoesTheGPLAllowNDA
http://www.gnu.org/licenses/gpl-faq.html#DoesTheGPLRequireAvailabilityToPublic

This applies also to any modifications or additions to Textpattern, and any integrated software or libraries that link with Textpattern code:

http://www.gnu.org/licenses/gpl-faq.html#GPLInProprietarySystem

A system incorporating a GPL-covered program is an extended version of that program. The GPL says that any extended version of the program must be released under the GPL if it is released at all.

In short: you can charge clients for providing a copy of Textpattern, plugins, modifications and addons. However, you must license all of that software to them under the GPL.

More information about the GPL license can be found in The GNU General Public License and Commentaries, and in this Wikipedia article.