basis is how much you put into an investment. So in a taxable account, if you buy stock for $1000, that is your basis. If the stock goes up to $1500, you will only owe tax on your gain (the amount over your basis).
For retirement accounts, basis is the amount you paid tax on before it went into the account. So if you put $5500 into an IRA and deducted it all, your basis would be zero. If you deducted none of it, your basis would be $5500.
If you had a 401k from an old employer, chances are that was all deducted from your pay pre-tax and you had no basis in it. If you leave the employer and roll it into an IRA then you still have no basis in that IRA.
The tricky part is that the IRS considers all of your IRAs to be one big IRA for purposes of basis. So if you have a rollover IRA with $10000 and no basis, and a traditional IRA with $5000 and $5000 in basis, the IRS will think that you have an IRA of $15k and $5k in basis, so they will treat every dollar you convert from IRA to Roth IRA as having 33 cents of basis, regardless of which account it comes from.