There isnt a whole lot of connectivity to the other entries in the series, the Emerald Herald states at one point that the same thing has happened many times here. This place your in has seen this story told many times, there is always a monarch meant to link the flames, a curse (hollows), and four great ones, and a chosen undead with the prophecy to end the curse and link the flames. There are some very good lore videos on youtube that explain the story in a pretty short time. DS1 and 3 are connected to each other more than 2 , its kind of a stand alone in the series with its story, other than the main themes.
Here is the best video summary ive seen.