Subrogation

If you were at fault in the accident--and based on what you write, you likely were, or at least would likely be legally found to be at fault; there is a strong presumption that the driver who hits another car from behind is at fault, since he/she should have been traveling at such speed and paying sufficient attention that he/she could have stopped in time--then an insurer who paid out to its insured (e.g. the other car) can sue you to recover the amount(s) it paid out. This is called subrogation. And if you were at fault, they will likely win.
Of course, the fact that they are suing you does *not* mean that you were at fault: despite the fact that you hit the other driver from behind, if the other driver was sufficiently careless and gave you no time/space to react, they could be at fault instead.
However to respond: you can pay the amount they seek; you can try to negotiate a lower amount and pay that; or you can defend the case on the ground that either you were not at fault or they are trying to recover an excessive amount (they can't recover more than the actual and reasonable costs of the damage, etc., even if you were at fault). An insurer will have an attorney, so if you try to fight the case without a lawyer, you will be at a significant disadvantage. So if the case is large enough (that is, the amount sought from you large enough) to justify hiring a lawyer, do so: let the lawyer negotiate and/or fight the case for you. If the amount is not enough to justify the cost of an attorney, you are probably best off either paying or trying to negotiate a lower payment or better paymnent terms (e.g. payment over time).