An instrumentalist believes that the purpose of a scientific theory isn't to describe an objective reality, but rather to effectively predict phenomena and solve problems. So the major consequence of this is that scientific theories are meaningless to the extent they deal with unobservable phenomena, or do not provide computable rules for predicting observable events. Insofar as I understand it, to an instrumentalist a scientific theory is a set of functions -- purely a practical instrument for problem solving. We get to bypass the realism-idealism debate, since an instrumentalist would discourage us from drawing any conclusions about ultimate "truth".
In other words, instrumentalism suggests the practical utility of a theory is primary, that theories are nothing more than predictive algorithms, and that our reliance on them is no proof of their transcendent verity but reflects only the degree to which the relevant theory has proven effective at solving problems and predicting observable phenomena (rather than the degree to which they describe the character of an underlying reality.)
In Conjectures and Refutations, Popper criticizes instrumentalism for being too mechanical, and plainly reductive with respect to "purer" sciences:
Instrumentalism can be formulated as the thesis that scientific theories - the theories of the so-called "pure" sciences - are nothing but computational rules (or inference rules); of the same character, fundamentally, as the computation rules of the so-called "applied" sciences. (One might even formulate it as the thesis that "pure" science is a misnomer, and that all science is "applied".) Now my reply to instrumentalism consists in showing that there are profound differences between "pure" theories and technological computation rules, and that instrumentalism can give a perfect description of these rules but is quite unable to account for the difference between them and the theories
Instrumentalism is an important position characteristic of pragmatism, alongside radical empiricsm and conceptual relativity. Consider the maxim of logic formulated by Pierce (which he called the "maxim of pragmatism" before the movement was even named):
Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object.
Pierce reformulated this several years later (Peirce, 1905, from "Issues of Pragmaticism" in The Monist v. XV, n. 4, pp. 481-499, see p. 481 via Google Books and via Internet Archive):
The entire intellectual purport of any symbol consists in the total of all general modes of rational conduct which, conditionally upon all the possible different circumstances and desires, would ensue upon the acceptance of the symbol.
In another excerpt from that document, this time clearly showing some instrumentalist-leaning concerns:
In order to ascertain the meaning of an intellectual conception one should consider what practical consequences might conceivably result by necessity from the truth of that conception; and the sum of these consequences will constitute the entire meaning of the conception.