1) Analog input cards are voltage sensing. So when the signal is current, a dropping resistor develops the IR drop which the analog input then 'sees'. This is usually a precision resistor (0.1-0.05%), because any deviation from the ideal is a proportional error.
Sometimes the dropping resistor is built into the analog input, other times it is added to the input terminals externally.
2) Since current measurement requires breaking the circuit to insert an milliampmeter, some people install an external resistor at some point across which they can measure the voltage drop for troubleshooting purposes (like badservo says).
3) Some current loop analog input resistors have a resistor value that is less than the minimum 230 ohms required for digital HART communications (used to configure field devices). For sites that frequently use HART, they'll install an additional resistor (not across the (+)/(-) terminals, but elsewhere in the circuit to get the minimum loop resistance needed for HART. These are not precision resistors.