Solarus engine is licensed under GNU GPL v3. Lots of quests made with the engine have been licensed the same, but it doesn't mean all quests need to be licensed under GPL.
The engine being GPL means that, first and foremost, it is free and open-source, and will forever be. Source code is available and you can read it and study how it has been made, download it, modify it, distribute it as it is, or modified versions.
You can modify the engine as much as you want. Every modification made to the engine, if you decide to make them public, should also be licensed with GPL (or a compatible license), consequently guaranteeing that these modifications are also free and open-source. You can't make a proprietary game engine based on Solarus.
You can modify the engine for your own purposes, i.e. for private use, as long as you don't distribute it. But if you distribute the engine or a modified version of it, then it must remain open-source. It ensures modifications (improvements, new features, bug fixes, etc.) will always be shared with the community, and everyone will benefit from it.
Conclusion: If you make a quest with Solarus and you don't need to modify Solarus, just use it as it is, and everything will be fine.
The engine just acts as an interpreter for the quests. Actually, you can license your quest files as any license, even proprietary. It means you can copyright your code and resources.
However, if you license them as proprietary, it means you should not use existing GPL Lua files. If only one file is GPL, all files must also be open-source, and licensed with a GPL license.
Note that proprietary does not mean closed-source, here. Currently, Solarus quests cannot be closed-source, because the .solarus file is just a zip archive that contains all images, musics and scripts.
Conclusion: Your quest may be licensed with any license, but be careful with what third-party elements you use in your quest.
Let's say you want to make a commercial game with Solarus, i.e. copyright your scripts and resources. Here are the legal requirements:
You must package the executable solarus_run unmodifed (or with modifications made public), along with your quest data file data.solarus (or your-quest-name.solarus), and all required libs.
You must provide a copy of the GPL license with the program, so that players are aware of their rights. A text file in the download package, or within an informative Solarus menu accessible by the player, are valid ways to do it.
You must include the Solarus source code, or make the Solarus source code freely available. An hyperlink to solarus-games.org is a valid way to do it.
You may license your quest as proprietary, but it currently cannot be closed-source. Players will be able to see the quest data file content. You can legally forbid modification if you copyright your quest.
You may preserve the Solarus logo at the quest start. It's a nice way to say thank you to the community.
Coincidentally, Solarus community has initiated a project called MIT Starter Quest. It contains only MIT-licensed Lua scripts and CC0 (a.k.a. public domain) resources. It means you can use these scripts and resources for proprietary commercial projects:
Some essential scripts like the one that handles multi-events or the dialog box have been re-written and licensed under MIT, so you can use them in a commercial project.