Why Bulk Import is faster than bunch of INSERTs?

BULK INSERT can be a minimally logged operation (depending on various parameters like indexes, constraints on the tables, recovery model of the database etc). Minimally logged operations only log allocations and deallocations. In case of BULK INSERT, only extent allocations are logged instead of the actual data being inserted. This will provide much better performance than INSERT.

Compare Bulk Insert vs Insert

The actual advantage, is to reduce the amount of data being logged in the transaction log.
In case of BULK LOGGED or SIMPLE recovery model the advantage is significant.

Optimizing BULK Import Performance

You should also consider reading this answer : Insert into table select * from table vs bulk insert

By the way, there are factors that will influence the BULK INSERT performance :

Whether the table has constraints or triggers, or both.

The recovery model used by the database.

Whether the table into which data is copied is empty.

Whether the table has indexes.

Whether TABLOCK is being specified.

Whether the data is being copied from a single client or copied in parallel from multiple clients.

Whether the data is to be copied between two computers on which SQL Server is running.