What are the different elements in Functions points?

The different elements in function points are as follows:

Internal Logical Files (ILF)
External Interface File (EIF)
Record Element Type (RET)
DET (Data element types)
File Type Reference (FTR)
External Input (EI)
External Inquiry (EQ)
External Output (EO) Letfs run in detail through each of them.
Internal Logical Files (ILF)
Following are points to be noted for ILF:

ILF are logically related data from user point of view.
They reside in Internal Application boundary and are maintained through elementary process of application.
ILF may have maintenance screen or probably not.

External Interface file (EIF)
They are logically related data from user point of view.

EIF reside in external application boundary.
EIF is used only for reference purpose and are not maintained by internal application. 
EIF is maintained by external application. Record Element Type (RET)
Following are points to be noted for RET

RET are sub-group element data of ILF or EIF.
If there is no sub-group of ILF then count the ILF itself as one RET.
A group of RET within ILF are logically related, most probably with a parent Child relationship. Example: - Supplier had multiple addresses and every address can have multiple phone numbers (see the image below which shows database diagrams). So Supplier, SupplierAddress and Supplier phone numbers are RET.


RET quantifies the relationship complexity of ILF and EIF. DET (Data element types)
Following are the points to be noted for DET counting:

Each DET should be User recognizable. Example in the above given figure we have kept auto increment field (Supplierid) for primary key. Supplierid field from user point of view never exists at all, itfs only from software designing aspect, so does not qualifies for DET.
DET should be non-recursive field in ILF. DET should not repeat in the same ILF again, it should be counted only once.
Count foreign keys as one DET. gSupplieridh does not qualifies as DET but its relationship in gsupplieraddressh table is counted as DET. So gSupplierid_fkh in supplieraddress table is counted as DET. Same holds true for gSupplieraddressid_fkh.
File Type Reference (FTR)
Following are points to be noted for FTR:

FTR is files or data referenced by a transaction. 
FTR should be ILF or EIF. So count each ILF or EIF read during process.
If the EP is maintaining an ILF then count that as FTR. So by default you will always have one FTR in any EP.
External Input (EI)
Following are points to be noted for EI:

Itfs a dynamic elementary process [For definition see gDynamic and Static Elementary Processh] in which data is received from external application boundary. Example: - User Interaction Screens, when data comes from User Interface to Internal Application.
EI may maintain ILF of the application, but it is not compulsory rule. Example: - A calculator application does not maintain any data, but still the screen of calculator will be counted as EI. 
Most of time User Screens will be EI, again no hard and fast rule. Example: - An import batch process running from command line does not have screen, but still should be counted as EI as it helps passing data from External Application Boundary to Internal Application Boundary.
External Inquiry (EQ)
Following are points to be noted for EQ

Itfs a dynamic elementary process in which result data is retrieved from one or more ILF or EIF.
In this EP some input request has to enter the application boundary.
Output results exits the application boundary.
EQ does not contain any derived data. Derived data means any complex calculated data.