The lore is pretty voluminous, incorporating a storyline form the 1984 game, through Frontier and First Encounters, to the current game.
Each Power is fleshed out with a bit of character text, a flavour quote and a basic philosophy (with that philosophy reflected in how it secures control and expands - socially, militarily or economically). Each minor power (system governments ranging from a single station to full system control in scope) have a small amount of lore about who and what they are (corporate government of X system that does Y), but the sheer volume of these (4 per system average) makes up for that. It should be noted that this means that by running missions for a given power you can change the governmental make up of a system over time and cause all sorts of trouble (lock downs, civil wars, and if the baleful eye of FDEV community management notices, possible community goals).
between power and minor factions, are community goals. These are always lore driver tasks - grand expeditions, station builds, a major factional tussle over an independent system. They get a lot of in game news air time and actively shape the story. They usually have simple objectives, like 'ship metal here' or 'kill targets' and sometimes have an adversarial mission to thwart your attempts running in parallel. These are the most dynamic/noticable of the real time lore development events.
Lastly you have the major powers, monolithic, grasping power structures. You can see a collection of common sci fi tropes - The corporate and corrupt democratic Federation, the folksey and well meaning but naive Alliance, and the sepratist Empire with its lawless seators and slavery as a social safety net (revelling in the rich/poor divide as the natural order - but valuing benevolence as a virtue... one not always shown by the betters in society).
These have a wealth of lore and are fairly staticin terms of player ability to change much of that, but each power's major personalities are present as Power Play characters, adding further depth. Shadow President Winters and President Hudson reflect economic imperialism and military might respectively, and their success and/or failure in powerplay will be sure to have an affect on how the lore plays out.
Finally, you can keep up with all lore developments since release via the in ship GALNET link, which brings all of the latest news, with handy banner pics giving instant recognition of the content (powers have the personality on a thematic background (haulers for trade, stations for territorial news, ships for military and so on). Sometimes used for rule of cool, these banners make identifying stories of interest easier most of the time. They are also release almost daily, with some days bringing up to half a dozen related stories.
FDEV really want the space to feel alive, and though the game bears its warts somewhat uncomfortably at the moment, engaging lore and player involvement in the storyline is by no means lacking. Mechanics need a lot of spit shine and rework (the grind is real), but the story and living universe are working as intended.