I would first check the query plan of a single insert to understand the costs associated to that operation - it is not known from the question whether the insert is selecting the data from elsewhere.
I would then check the table indexing for the following:
- how many indexes are in place (apart from filtered indexes, each index will be inserted into as well)
- whether a clustered index is present or are we inserting into a heap.
- if the clustered index key means we will be getting a hotspot benefit on the end of the table or causing a large quantity of page splits.
This is all SQL schema based issues, assuming there is no problems within SQL, you can start checking disk IO counters to check for disk queue lengths and response time. Not forgetting the Log drive response time since each insert will be logged.
These kind of problems are very difficult to nail down as any 1 perscriptive thing / silver bullet you can give advice over, just a range of things you should be checking.