By now you know that the "l" at the beginning of this word is a prefix meaning "to."
"Tzion" is a proper name which in English is rendered "Zion." It is from this geographic name that the word "Zionism" eventually emerges. The origins of the name are shrouded in historical mystery. Though there are words in Hebrew meaning "stone" and "marker" and "dry" that share the same letters, the mountain that is part of Jerusalem seems to be known by Tzion without the same symbolic background as Mt. Scopus or the Temple Mount.
Maybe for that reason, the Biblical prophets used Tzion when they referred to Jerusalem (and, by extension, the entire land) as a place of spiritual nurture, a place where the presence of God rises with the topography. Throughout the centuries, the poets of our people in four corners of the earth used Tzion to symbolize the yearning for restoration to our homeland. For that reason, it is unsurprising and appropriate that Tzion turns up in the prayer book in general and in the Amidah in particular when a proper name for "the Land" is needed and when reference to the spiritual qualities of Jerusalem is desired.
It also helps explain why it was that the nineteenth-century political movement among the Jews in Europe chose the name Tzion for their ideology. Zionism is not just the longing for any Jewish homeland, it is the understanding that there is a spiritual quality to being a people in its own land. In fact, there was long discussion about whether the proposed Jewish state would be called Zion or Israel. For a variety of reasons, well-discussed in Zionist literature, the older and better-known Israel was chosen.
Of course, the presence of Tzion in the prayer book predates modern Zionism by many centuries. It is not modern Zionism that adds meaning to the Amidah, but the Amidah that adds meaning to modern Zionism. Still, there is no denying that a Jew today appreciates the reference to Tzion with an extra layer of meaning than was ever possible for thousands of years.