On an Ungrounded system, there is no Intentional Connection of the system to Earth Ground (or to enclosures Intentionally Bonded to Earth Ground), through either a Solid Connection or an Impedance / Resistance.
This means there is no physical Bonding of the Power System
(such as the Secondary Side of the Transformer delivering AC Power from the Utility Company)
to the Earth Ground / Metallic Raceways and/or Enclosures.
The Metallic Raceways and Enclosures WILL be Bonded together, and connected to a Locally Established Grounding Electrode System, but the Power System will not be connected to these items - hence the System is "Ungrounded".
The Power System may, or may not, incorporate the use of a "Neutral Conductor" - depending on the configuration; but still no Conductor is Intentionally Grounded, and the System has no "Grounded Conductor".
The most common configuration used for Ungrounded Systems (at least in my area - So. Calif.) is the Ungrounded 3 Wire Delta. Voltages of 480 VAC and 600 VAC, but may be some 240 VAC systems out there too.
Although Grounding a System does not achieve any merit in normal performance, it does effect the stresses imposed on Insulation and such.
An Ungrounded system may have an extremely high Potential to Ground at different points along the system's connected Equipment - at times exceeding the nominal rated Voltage by maybe 3 times as high!
This is due to Capacitive Coupling effect between the Power System's Conductors and the Grounded surfaces / Equipment / etc.
A Grounded System (solidly or through an Impedance / Resistance), will stabilize the Potential to Ground, thus reduce the Insulation Stresses.
Much more to cover on this stuff, and other Members can explain much better than I, so feel free to reply for additional info.
Also check the Technical Reference Section for Schematics, additional information.