These are giant towers which touch both the bottom of the ocean and the top of the sky.
Each obelisk has glyphs on them. Once activated, the glyphs turn a bright blue and allow passage of people, information and vessels to other nearby obelisks.
Few races have ever tried to damage these. And no one has ever really succeeded.
The best academic minds across races have only unlocked the usage of the glyphs to allow transport. No one has ever really understood what magic it uses and how it works.
These obelisks are believed to built by the Protheans.