The planetary phenomenon when the shadow of the Earth falls on the Moon is known as Lunar Eclipse.
During Lunar Eclipse the sunlight to the Moon is blocked by the Earth. The light reflected through the Earth's atmosphere makes the Moon visible during Lunar Eclipse. If there was no reflected light through the Earth the Moon would have become invisible during Lunar Eclipse. Due to reflected light from the Earth, the Moon looks reddish during Lunar Eclipse.
The shadow of the Earth, which falls on the Moon during Lunar Eclipse, can be divided into Penumbral and Umbral regions. Due to property of Physics all planetary shadows form two regions which are known as Umbra region and Penumbra region. From diagram it is clear that Umbral region is dark as no sunlight reaches to this region while Penumbral region is not fully dark as some sunlight reaches to this region.
When the Moon comes under Umbral region completely Total Lunar Eclipse is observed from the Earth. If the Moon passes partially through the Umbral region but doesn't pass it completely then Partial Lunar Eclipse is observed from the Earth.
Penumbral Eclipse occurs when the moon passes through Penumbral region of the shadow without touching Umbral region of the shadow. Penumbral Lunar Eclipses are of less important and often go unnoticed as those are not visible to the naked eye. Hindu calendar does not even list Penumbral Eclipse and ignores it completely.
It should be clear by the diagram that during Total Lunar Eclipse, Eclipse starts with Penumbral phase, moves to Partial Umbral phase and finally moves to Total Eclipse phase. Moon remains under Total Eclipse phase for some time before returning back to Partial Umbral and subsequently returning back to Penumbral phase before coming out of Eclipse completely.
It is interesting to note that at some locations on the Earth a Total Lunar Eclipse or a Partial Lunar Eclipse might be observed as a Penumbral Eclipse only. It happens when moonrise occurs when the Moon has come out to Penumbral region from Umbral region or when moonset occurs when moon is just about to move into Umbral region from Penumbral region. Similarly at some locations on the Earth a Total Lunar Eclipse might be observed as a Partial Lunar Eclipse due to same reason.
In a year there might be total 0 to 3 (0 and 3 inclusive) Lunar Eclipses. Total Lunar phase of an Eclipse lasts for one to two hours and total length of complete Lunar Eclipse from Penumbral to Penumbral is about four to six hours. A Lunar Eclipse has almost equal probability of being Total Lunar, Partial Umbral/Lunar or only Penumbral one.
Scientifically it is safe to watch Lunar Eclipse with naked eye either during Partial Lunar phase or Total Lunar phase of the Eclipse.