By default, the Mapillary mobile apps capture images with the largest resolution, at 4:3 ratio. Depending on your device, one image takes roughly 2-8 MB, giving you about 1000-4000 images if you have 8 GB of free storage on your phone. The average file size on iOS devices for each image is about 2 MB; on Android devices, it is generally a bit larger so you may need an external SD card (you can change the storage location in the Settings).
If you have concerns about the space required, you can use Settings to reduce the resolution of the images or the frequency of capture. On Android devices, by default capture will be stopped when you have less than 10% free storage space left, or when your battery level is under 10%. The iOS app has no battery warning but will stop capturing at 1% free disk space by default. You can change these values in Settings too.
Images are stored in the app folder and deleted after upload. Images are never stored in your camera roll/album. The only way to view them is through the upload view in the app. This also means that if you want to keep copies of the images, you need to do this before you upload.