A "rollover" is when you withdraw funds from an IRA or plan and contribute those funds to the same or another IRA or plan. A "trustee-to-trustee transfer" (often called a direct transfer or direct rollover) is when you never receive the IRA or plan funds. They are transferred directly from one financial institution to another without you ever touching the money.
The general rule is that when you take a distribution from an IRA (or other tax-deferred retirement account) that you intend to roll over, it must be contributed back to an IRA (or other tax-deferred retirement plan) within 60 days.
When you transfer funds between IRAs or between a pension fund and an IRA, you can request a direct transfer from one account to another. Or, you can have the money sent directly to you. You can transfer your money from one IRA to another without paying taxes or penalties. The IRS allows only one such transfer where the money comes to you first in a 12-month period. However, if you transfer money directly from one institution to another, or one fund to another, you can make as many changes as you want.
You might consider this kind of transfer if you want to consolidate your IRAs for easier management. This is also a good option for those who aren't satisfied with the earnings on one IRA and want to switch to a better performing account.
Transferring your funds from a Traditional IRA to a Roth IRA is a two-step process. First, you must withdraw your money from the Traditional IRA and pay taxes on the withdrawn money. Then, you can use your after-tax money to open a new Roth IRA. Consult with a financial expert to make sure such a conversion is beneficial to you.