This question is more suitable for the Lore forum, but at a very basic level, to answer your question, (and spoilered),
it's basically 'jailbreaking' the soul - specifically, allowing your mind and soul to "go beyond the boundaries of the flesh", and allows you to interact and even manipulate others' minds and souls (hence why you can view others' memories and instinctively know foreign languages you had no physical knowledge of), and also allow your own soul to break out of it's own limits, and preventing such aetheric manipulation on yourself in kind (as in, it grants immunity to Primal tempering).
Mastery of the Echo basically allows you to become a being of pure aether that no longer requires a physical form to sustain and can thus overcome physical death (like how the Ascians do). Shadowbringers revealed the Echo is actually a fragment of the Creation Magic power the Ancients possessed naturally prior to the Terminus and the Sundering, so everyone that is 'awoken' to the Echo was once an Ancient soul 12000 years before and not a 'new' soul born after the Terminus rewrote the laws of nature (this is why the Ascians also possess it while simultaneously mocking it like Lahabrea did, to them it's a mere sliver of the almost divine power that it used to be)
As for the Blessing of Light, the two are connected but also seperate. The Blessing something specifically granted to you by Hydaelyn and is basically a direct 'hotline' to her, allowing her to more easily interact with you and also allows you to materialize Crystals of Light that further empower the mandala and strengthen it.
There is still a lot of unknowns about it however.