In the United States, any creative work - including images, music, and artwork - is copyrighted from the moment it is completed (17 USC, Section 102). Similar laws apply to websites hosted in other countries, so you should assume that every image, word, sound, and piece of software you find on the Internet is under copyright.
How this applies to you: If you wish to include other people's words, artwork, or images in your honors thesis, you must seek permission from the copyright holder. In addition, you should always cite your sources.
If you are looking for content to support your honors thesis, you may want to consult this guide, which considers copyright restrictions as they apply to images, artwork, and images found online.
If you are seeking images for your honors thesis, it may be useful to know that - in some cases - content creators allow more liberal reuse of their work. These creators specify how their work can be reused using Creative Commons (CC) licenses. Creative Commons can be a useful source of images for your project, but please respect the creator's preferences when using this content, which is searchable on the Creative Commons website.
This Ars Technica post from 2011 is a good general guide to the use of Creative Commons images: Creative Commons images and you: a quick guide for image users.
You can also read more about the Creative Commons here and here.