An emergency fund is cash that you set aside so that you have some money you can use quickly in the event that something unexpected happens in your life. This includes sudden medical bills, loss of job or a car repair.
For most people an emergency fund of 3-6 months of expenses is suitable. You may want a larger emergency fund of 9-12 months of expenses if you have unstable income. You may want to temporarily have an emergency fund of $1k or 1 month of expenses if you are trying to pay off debts like credit cards and loans.
You want to keep your emergency fund somewhere you can access quickly which means you can put your money in a savings acounts, a checking account or a money market savings acount. CDs (offered by most banks) and I-Bonds offer higher interest rates and can also be used for your emergency fund but they are less liquid so they should be used for only a portion of your emergency fund.
If your income is stable, you are young or you just think you can take on a little bit of risk then it could also make sense to invest your emergency fund with a portfolio of 30-50% stocks and 70-50% bonds. This way your emergency fund can really grow instead of just earning a little bit of interest in a savings account. You can do this by using a robo-advisor a Vanguard LifeStrategy Fund or a Lazy Portfolio. As these investments grow and your emergency fund becomes too large, you can withdraw some of it and use it elsewhere. Obviously, investing your emergency fund does come with some risk because your investments may drop in value.