With a direct rollover, the check from your employer sponsored plan is made out to the financial institution where you opened your IRA, for the benefit of you. Since this money is deposited directly from the 401(k) or other qualified retirement plan to the IRA, no taxes are withheld.
With an indirect rollover, the check is made payable to you. Your former employer withholds a mandatory 20% for taxes. You have 60 days to deposit these funds into an IRA, and must make up the 20% yourself, otherwise the 20% withheld will be considered a taxable distribution and only 80% will have the potential to continue to grow tax-free or tax-deferred. In addition, if you are under age 59½ you may be subject to a 10% additional federal tax, unless one of several exceptions applies.