Hotly contested among financial experts is the question of whether it is better to use your extra money to pay down your debt or to save for emergencies. There are valid arguments to both strategies, but the fact is that if you have no money at all in savings, no emergency fund to speak of, than your priority must be to immediately save some money.
Paying down debt faster can save you money on interest, but any gains from that strategy can quickly be whipped out with one simple emergency. If you have no money in the bank, unforeseen medical bills, car trouble, or major appliance repairs can put you in a desperate state. Sometimes you can put it on a credit card (more debt), or you might end up missing other bills (late fees, possibly negative credit reporting, etc.).
A true emergency fund should have around three months of income saved. That might not be a feasible savings goal until you have been able to pay off some of your debt. But it is absolutely a smarter idea to save some sort of basic emergency fund to provide the very necessary cushion of our unpredictable lives. Saving a minimum of $1000 is the first financial step for any situation.