A checking account is one of the many different accounts that banks offer. A checking account usually pays no interest, or very little, so it's not the best place to put your hard-earned savings. What it does offer is convenience. A checking account is useful for money that you will be spending soon. Many people use a checking account to pay their everyday bills.
With a checking account, you can deposit money in the bank. Then when you are ready to spend some of it, to pay your electric bill for example, you write a check. You send the check to the electric company. When the electric company cashes the check, the bank takes money out of your account and gives it to them.
What bank should you choose for your checking account? That's up to you, but there are a few things you might want to consider. One thing is the bank's location; does the bank have a branch at a convenient location near your home or work? Another thing is the bank's schedule; is it open at hours when you will be able to get there? You also might want to consider whether the bank has an online banking option or even online bill paying. And it's a good idea to find out whether the bank offers a free checking account or whether there will be fees to pay.
There are also online banks that have advantages and disadvantages of their own. An advantage of some online banks is that they might pay a small amount of interest on a checking account. A disadvantage is that there is no one you can visit in person to talk to about your account.