The actual phones get the most attention at Mobile World Congress every year—the Samsung Galaxy S7, LG G5, and Xiaomi's Mi 5 all look promising in different ways—but component announcements can give us some insight into what to expect later this year and at next year's MWC. For example, Samsung has just announced 256GB NAND flash chips suitable for phones and tablets, many of which top out at 128GB today.
The capacity is interesting, but Samsung spends more time extolling the virtues of the Universal Flash Storage (UFS) 2.0 interface used to connect the storage to the rest of the phone. By using a two-lane storage interface, these chips promise sequential read speeds of up to 850MB/s and sequential write speeds of up to 260MB/s; the read speed is quite a bit higher than the mainstream SATA III SSDs available for many PCs today. The write speeds are likely capped because you can't fit as many flash chips into a phone or tablet as you can into a dedicated SSD, and SSDs need to be able to write to multiple flash chips at once to maximize performance.
UFS is just one possible solution for speeding up mobile storage. Apple, for instance, is using an NVMe interface for storage in its latest iPhones, the same interface that it's using for SSDs in newer products like the MacBook and Retina iMacs. Either way, the interface leads to better performance in phones and tablets, and (as Samsung points out) combined with USB 3.0 interfaces, it can improve transfer times when you're moving files over from a PC. Both can be considerably faster than the eMMC interface, which is still what is used most frequently in phones, tablets, and even low-cost laptops.