Obelisks in Rome often have "nicknames" based on their current location. So this one, the Lateran Obelisk, obviously stands near San Giovanni in Laterano. If you are only casually familiar with Rome that name might still ring a bell. The Lateran Palace stands next to the Lateran basilica, and was the site of several "Lateran Councils" in medieval times. But back to the obelisk.
This one has a lot of superlatives attached to it. It was the tallest obelisk brought to Rome. Also the last one. It is perhaps the best preserved. It was the last one to be restored and re erected.
The obelisk was originally put up by Pharoah Thutmose IV at Karnak. It was brought to Rome by Constantius II when he made his only trip there in 357 AD. By that point Rome was no longer the unquestioned center of the Empire, Constantinople or wherever the Emperor and his army were at the moment tended to be the true capitol.
The obelisk sat in the spina of the Circus Maximus until the end of the Empire. At some point it fell and was buried under silt and debris.
Pope Sixtus V had it restored and moved to its current location in 1588.
There is actually an ancient account of the transportation of the obelisk from Egypt to Rome, found in Ammianus Marcellinus. Its a bit long to cut and paste here but worth the read. It sounds as if the obelisk came into the city via the Porta San Paulo, then known by its earlier name Porta Ostiensis.