Can someone smarter than me explain what this means in simpler terms? I feel a bit lost after reading this, I hold triple citizenship (Canadian, Slovak, UK) and live in the UK, but not sure how this affects me
I am not a lawyer, nor do I know more details, but I would guess it should not change anything for you, as your slovakian citizenship should suffice.
[edit] first version was missing a crucial „Not“
The only thing that changed is that UK nationals no longer have the status of "citizen" in the EU (unless they have dual citizenship, of course). What that means exactly differs per country.
IANAL but I don't think this changes much in practice, or was ever an unexpected outcome, really.
As Slovakia is a member state of the EU, this will not itself directly affect you.
The question that arose after Brexit was, whether British citizens would possibly retain this citizenship, which could have meant that they would retain the rights that come with it as well. There are different arguments why British citizens might have kept this EU citizenship, for example it might be argued that the withdrawal of a _state_ from the Union can not mean that _individuals_ loose their rights or it could be argued that such a loss of rights would be disproportionate.
The CJEU has now interpreted the treaties in such a way that the withdrawal does indeed mean that individuals loose their EU citizenship, arguing that "the authors of the Treaties thus established an inseparable and exclusive link between possession of the nationality of a Member State and not only the acquisition, but also the retention, of the status of citizen of the Union".
So this ruling might have had a big effect if the CJEU decided in a different way. The way they decided now, everything stays the same. If you are in possession of another EU member states citizenship (Slovakia) this will not change anything for you, you will remain an EU citizen.
[1] Technically many of those rights were already in the treaties before the introduction of the EU citizenship, so it is a bit "declaratory" in nature.
Long story short, EU citizens have certain rights in some member states. When the UK left, UK citizens are no longer entitled to any rights given to "EU citizens" in their country of residence.