A well stocked emergency fund will go a long way in reducing your stress in life. Next time you need new tires? No problem, you saved for that. Next time your appendix burst and they don't remove it all during the first surgery so you have to go back into the OR for a second surgery (just me???)....no problem! That's what savings is for! Some people call an emergency fund "peace of mind savings" but no matter what you call it; it's really nice to have. Now, plenty of people will argue about how much you should have in there but the common advice is 3-6 months of expenses, minimum. More or less based on your risk tolerance.
For most US household this number will fall between $8,000 - $20,000. As always, I encourage you to look at your finances and figure out what it would be based on your spending habits. No matter how you calculate it you'll realize that's a hefty amount of money you'll want to save! I recommend starting with what you can, find a way to save $5 a day - should be easy right. You could skip the coffee, pack your lunch, cook at home, make your own lotion, etc. These will all easily start saving money, FAST. After a year you'd be able to add $1,825 to your emergency fund and I bet you'd start enjoying watching that number grow and find even more areas of your budget to cut.
The point is, hearing that you need a 5 digit emergency fund can sound really overwhelming and intimidating when you're just starting out on your financial journey. However, if you start small and stay committed you will see that number grow faster than you ever imagined. You'll start making small decisions to save hundreds of dollars and before you know it you'll have $10k+ in the bank and be ready to start investing. Believe me, that's when the real fun begins!