The method by vembutech is a definitely a more polished solution. Here is a lightweight VBA macro that would export all the sheets from one workbook.
Goes in the active workbooks folder all names are workbookname_sheetname.csv
Sub exportcsv()
Dim ws As Worksheet
Dim path As String
path = ActiveWorkbook.path & "\" & Left(ActiveWorkbook.Name, InStr(ActiveWorkbook.Name, ".") - 1)
For Each ws In Worksheets
ws.Activate
ActiveWorkbook.SaveAs Filename:=path & "_" & ws.Name & ".csv", FileFormat:=xlCSV, CreateBackup:=False
Next
End Sub
EDIT:
For the comment. The original macro simply uses the save as function (which is sort of like closing the original). If you want to do this while leaving the original open you need to copy to a new workbook, save, close the new workbook.
Sub exportcsv()
Dim ws As Worksheet
Dim path As String
path = ActiveWorkbook.path & "\" & Left(ActiveWorkbook.Name, InStr(ActiveWorkbook.Name, ".") - 1)
For Each ws In Worksheets
ws.Copy
ActiveWorkbook.SaveAs Filename:=path & "_" & ws.Name & ".csv", FileFormat:=xlCSV, CreateBackup:=False
ActiveWorkbook.Close False
Next
End Sub