Yes, the Edison has a 4GB emmC of flash storage as can be seen in the Product brief http://download.intel.com/support/edison/sb/edison_pb_331179002.pdf .
You can use this memory without the need of an SD card. If you need more storage space there’s the option of using an SD card. You’d have to do some modifications and basically follow this guide How to boot Edison from an SD card (Linux) so that you are able to use and boot from the SD card.
Let me know if this was helpful.
What do you mean with endurance? If you refer to how long will last the data stored in the emmc then it’s not supposed to be erased just because. The data written in the emmc will be stored until the user decides to erase it, so there won’t be issues if you don’t wish to use an SD card procedure described above.