Let's imagine that you expect to have 1A of current going through your circuit.
Resistor of 0.1 Ohm will give you a voltage drop of 0.1V.
This causes two problems.
Firstly Arduino has a cheap ADC builtin. It's supposed to be easy to use, but not really precise. It has nonlinearities towards lower and higher range. You will get more precise reading when measuring voltages around 2.5V.
Secondly The precision of your measurement is cut by factor of 50. Arduino contains ADC that has resolution of 10 bits. This means that there are only 20 steps between 0V and 0.1V That's not really precise.
Solution? Use an opamp as "differential amplifier". If you multiply the voltage difference by 25 you will get 2.5V on the amplifier output when the resistor has 0.1V of drop on it. This value is much more precise when reading it by analogRead of the Arduino, and even a tiny change in voltage on the resistor will give you 25 times larger change on the amplifier output. This way it's much more precise and accurate.