Short answer is an ideal measurement instrument does not perturb the system it is measuring and produces a completely accurate rendition with infinite precision.
Real instruments always change the system to some degree and have finite sensitivity, accuracy, and precision and generally have some noise level.
In the case of a typical ammeter the primary issue is that it introduces additional resistance (RA in your example) as opposed to zero ohms into the circuit path. It will also have frequency limitations and will introduce additional parasitic components (capacitance, inductance) into the circuit that may change the performance of the circuit unintentionally. The latter generally is a problem in RF and sensitive circuit nodes.