WordPress is one of the most if not the most popular platform to write in the web.
Mobile is growing fast and that also is for writers who would like to write without have to be in front of the computer.
What do I need?
For WordPress nothing more than one of their mobile apps, so far they have iOS and Android versions, you can check and download them here
The apps not just for write, but also you can check comments made on any of the sites you are author or admin, you can check statistics from Jetpack (if you use it) and read blog from WordPress.com you follow.
The apps also notify you when your stats are going up, also if there is a comment that needs moderation, to save a draft for the articles that you may have started to write.
You can add images, any post type, and also a featured image, directly from your device, taking the photo or upload a previously taken picture.
The team behind the apps are constantly working on improvements, the blog about them, and it is a active community
Of course the apps are free, and you can contribute to them from the web listed before.