Ytterbium is not very important. Only about 50 metric tons of the stuff is produced each year. That being said, element number 70 is part of a group of important, high-demand elements. They were once called “rare earths” but it turns out these substances are neither rare, nor “earths” (the old name for metal oxides).
Although the old term “rare earths” is still widely used, chemists call these elements lanthanides after element #57, lanthanum. There are 15 lanthanides, from #57 to #71, lutetium. They occupy the 4f-block of the transition metals. It is more correct to say lanthanoids as the “-ide” suffix is normally used for negative ions, but the usage of lanthanide is so pervasive that it will likely stay.
The word means “to lie hidden.” Many of these elements were unknown until modern times because they are so chemically similar they are hard to separate and distinguish. Ytterbium is named for Ytterby, Sweden, which is where it was first isolated. The elements terbium (Tb, #65) and erbium (Er, #68) are named for the same place.
Ytterbium is used in atomic clocks and in fact is part of the world’s most accurate time piece. Some ytterbium is used as a moderator in nuclear reactors. Otherwise its sister elements in the lanthanoid series are the ones getting the headlines. They are used as catalysts in glass-making and in optical devices like lasers. Mostly they are used in magnets and electric motors. Right now the US has only one rare earth mine and one processing facility. China is the world’s leading producer.