The Forum's Curia was the meeting place of the Roman Senate. According to tradition, it was originally built by Tullo Ostilio, the third of Rome's seven kings, and later rebuilt by Silla in around 80 BC. Julius Caesar moved it to its current location where it was subsequently modified by Augustus, Domitian and Diocletian, before being converted into a church in the Middle Ages. The brick barn-like construction you see today is a 1937 reconstruction of Diocletian's building.
The bronze doors are copies – the originals were used by Borromini for the Basilica di San Giovanni in Laterano.