There are at least two sides to what is happening today: the political and the spiritual.
Politically, it is difficult to know. In some senses nothing is happening today, except that a process will start: i.e. today we begin the process that was promised (by the then Prime Minister) to start on 24 June 2016, more than three and a half years ago.
In particular, the core issue why so many people wanted Brexit - the imposition by the EU of everlasting, accelerating, uncontrollable mass immigration - is not changing today. And the current notion seems to be that Britain will remain shackled and subservient to the EU in several importantly-harmful ways.
Here is a summary of the politics of Brexit - on a blog of Christian Prophecy, whose writers are well-motivated, but not necessarily expert insiders (the two categories nowadays being incompatible). The link includes a 90 second video of how the UK came to join the EEC and why we left the EU - again from a political angle.
Spiritually... well, that's where things are interesting. If Brexit is understood, by 'The People' to be a genuine separation, a new era; a restoration of sovereignty in a spiritual as well as a political sense; then today will be just the beginning of a process of changing expectations and desires that will continue... and who knows where that process, once begun, will stop?
If the EU has now, today, lost legitimacy in the eyes of The People; then every time there is an assertion of power from the EU (or from the Establishment, citing EU directives), then it will be challenged, there will be resistance: push-back. Under such a situation, the process of separation will continue, increase, feed-upon-itself: become unstoppable (whatever today's treaty says).
If the people of the UK - specifically the people of England - who are primarily driving Brexit* - have a solid sense of national spirit; and if they like and are motivated by that the feeling of restored national spirit... again, today will be just a beginning.
So today, Brexit Day, may mean nothing significant; or a great deal - nothing much or the beginning of a new era.
Nobody yet knows. Only time will tell.
Each person has a role to play by the nature of their response - not the Establishment, because they will not change, they actively-want the UK to be part of an EU Leftist (anti-Christian) superstate with totalitarian powers - but everybody else will determine whether by their response whether this merely means aspiring for a non-EU totalitarian Leftist State (like Canada, Australia, Norway, Switzerland etc.) - or... something qualitatively different and better.
Will the ball start rolling; or stay pretty much where the current treaty has placed it?
*Note: This English distinction is important. The Scots are enmeshed in a very different political and societal crisis than the English. Most English people (except the Establishment) would now prefer to end the political union; feeling that the link to Scotland does us more harm than good.
Scotland is more fully Leftist, statist, keener on totalitarianism, and increasingly motivated by un-assuage-able resentment against England - none of which has gone unnoticed by the English. Wales is mildly pro-Brexit and pro-continued union with England; but has similarly become psychologically-organised around anti-Englishness. The vehemently (notoriously) anti-English proportion of Northern Ireland is already and increasingly dominant, and the future of that union is also doubtful.
But, for the first time in many generations, England is stirring; and not driven by resentment but by a desire for survival that has triggered a positive patriotism for something that is not-clearly-defined by more clearly valued than for a long time.
As of the recent General Election; the Labour-Conservative division has all-but disappeared, to be replaced by a division between the pro-totalitarian Leftist Establishment (or all parties) and the an amorphous and inarticulate 'English people' - who don't really know what they want, are poorly motivated (because irreligious) - but are pretty clear about what they don't want.
All that can currently be said in favour of the pro-Brexit mass is that it is not as explicitly and strategically evil as the pro-EU Establishment; but this is a more hopeful situation than if the English masses had been positively in favour of the Establishment's plans for a Euro-State of omni-surveillance and micro-control.
It is from among the pro-Brexit English masses that we may look for, or at least hope for, an impulse of Christian renewal - which is certain to be individual at first, and likely to be small scale at best - but is far preferable to the alternative.