Genestealer Patriarchs are often the founders and leaders of the Genestealer Cult and are identified back in the early days as the big fat fuck sitting on his chair. Of course with the revamped and revived Genestealer Cults as of 2016, they now look like regular old Genestealers, albeit bigger and more robust. I guess big papa Genestealer has been picking up on leg day after over a 20 year absence. What? Genestealers can be fat shamed too; I mean it's not like they can blame it on their genes.
The Patriarch is always the oldest purestrain of the cult. As the first Genestealer of the group, all other members are psychically linked through it; this leads it to attain a level of intelligence much higher than that of other Genestealers. Over time, it can become a very powerful psyker; it grows in size and strength, gaining a bloated and immobile appearance.
However with the new information given out, their fatass has been retconned and now Patriarchs are twice the height of a Space Marine, armoured with an incredibly tough Carapace shell and with strength enough to slice an Ogryn into bloody chunks, this creature is now a leering nightmare of tooth and claw rather than a laughing gag. In a flurry of whipping limbs and diamond-hard talons the Patriarch can tear through platoons of heavily armoured warriors and even light vehicles. Yet it is the hypnotic spell with which it binds its chosen hosts that mark it out as perhaps the most dangerous Tyranid yet encountered by the Imperium. The uncanny powers of the Patriarch make it a fearsome puppet master, a threat so pervasive it has a xenocode threat designation unto itself. By spreading the Genestealer Curse, this creature is capable of destroying not just warriors and war machines, but entire worlds.
A Patriarch whose cult is on the verge of taking over a world becomes a psychic beacon, attracting Tyranids to the planet; as the Tyranids approach it will fall under the power of the Tyranid Hive Mind, and begin leading the cult in attacks on vulnerable positions to facilitate the inevitable invasion. It is assumed that it either knows nothing of its role in the Tyranid invasion or doesn't care, for once the Tyranids are successful, it and the brood are also consumed by the Hive Fleet.
Patriarchs are known to live for hundreds of years, and unless killed, are practically immortal. They are seen by the cult as a "father" figure, and should their destruction come to pass, the cult would be thrown into disarray. Eventually, however, the next oldest purestrain genestealer would assume the role of Patriarch.
The 8e codex confirms that the Broodlord and the Patriarch are not related; the Broodlord is empowered only by its own brood of Genestealers rather than a full-fledged cult. 8th edition also brought about another odd retcon: two Patriarchs could exist on sufficiently large planets and somehow the cults wouldn't have an issue with this.