For a long time, it's been thought that the largest a star can physically get is 150 solar units, or 150 times more massive than our sun. That was before we discovered R136a1, a star nearly 300 solar units large. What the heck is going on?
The massive star is in a cluster of equally-massive stars called R136. Many of the young stars in this cluster were greater than 150 solar masses at birth, tens of times larger and several million times brighter. This particular one appears to have been born at a whopping 320 solar masses before shrinking to its current observable size of 265 solar masses (stars shrink as they age, unlike humans).
Before the discovery of the cluster, the largest it was thought a star could get was 150 solar masses. Because as stars get larger, the amount of energy created in their cores grows faster than the force of gravity that holds them together, making them increasingly unstable as they get bigger. It's not entirely clear how this star is keeping together, but the chances are good that it's highly unstable.
What would happen if our sun was that large? We'd be dead, to not put too fine a point on it. Let's just be happy that these gigantic stars are far away from us and we've got a reasonably-sized one keeping us warm.