The land can now be tapped for black mana in addition to any other abilities it already has. This works just as if the text "{Tap}: Add to your mana pool" was added to each mana-producing land. In other words, the land can be tapped for its own ability _or_ it can be tapped for black mana. Not both.

Whether the land is a basic land or not is unchanged by this effect.

More than one Blanket of Night has no meaningful additional effect.

Anything which counts the number of Swamps on the battlefield will not double count an actual Swamp card while Blanket of Night is on the battlefield.

It can affect lands which do not produce mana.

The lands do not get the name "Swamp" in addition to their current name. This is a reversal of older rulings.

The ability is a land type change effect so it is ordered along with other land type change effects in the order they entered the battlefield.

If this effect is applied to a snow land, the land is now a snow Swamp and not just a regular Swamp.