The Dungeon Heart is a Keeper's hub of summoning operations. When minions are summoned, it is into this room that they will first appear.
The level of a Dungeon Heart affects the maximum levels of other rooms in your dungeon (gold mines, stone quarries, treasuries, stone storage depots, etc.), which will govern the amount of gold and stone that is produced and stored in your dungeon (both of which are needed to build/upgrade other rooms, etc.). This affects your ability to build some of the more expensive rooms, based on their build costs. Therefore, upgrading a Dungeon Heart allows for upgrading/building other rooms. Another benefit of upgrading your Dungeon heart is that doing so also provides for additional summoning portals, allowing for more minions to be produced at the same time.
Dungeon Hearts have more health than all other rooms - a feature that savvy Keepers might choose to exploit by occupying the attention of attacking minions while cleverly-placed traps do their work. Just be careful... destroying a Dungeon Heart counts as an immediate win for an opponent. By themselves, Dungeon Hearts have no inherent defenses, until its final level, where it acquires its own defensive measures.
Some might say that Keepers can be heartless. On the contrary, you do have one... and you'd better defend it, at all costs!