Modernism is generally this literary movement that lasted from the early 1900s till World War II that focused on attempting to gain meaning, truth, and beauty from creating art and literature, basically, trying to fill the void and save society by creating, and ultimately, re-defining, art. Think T.S. Eliot, Virginia Woolf, the Bloomsbury group, James Joyce, Ezra Pound. Thus, when most who explain postmodernism talk about its relation to modernism, they're probably talking about postmodernist literature and art, and how that differs from modernist literature and art.
But from a philosophical standpoint, most modernists believed in the notion that something could save society, while many postmodernists reject such notions. If you're a post-structuralist, the world cannot be saved because power structures dominate everything from creating roles for the individual to meaning in language. If you're a deconstructionist, society cannot be saved because most of society has placed its trust in an unstable, unreliable medium of communication: language itself. If you're Jean-François Lyotard, society cannot be saved because ultimately people living in societies tend to blindly trust the epistemology of that society without considering other cultural perspectives (i.e. how Western intellectuals embrace scientific reasoning without considering other cultural perspectives).
Another possible way of answering your question would be to liken modernism to metaphysics, as literary theorist Ihab Hassan did in "Toward a Concept of Postmodernism", and postmodernism to irony. The way metaphysics is used in Hassan's essay is basically the justification for the ability of scientific theories to explain the world. You start with observations about the world around you, and create theories to explain those observations, and select the one that best explains these observations. Hassan's modernist "metaphysics" would argue that theories that have been traditionally accepted were accepted because, simply, they were the best explanations of the natural world. Yet, the postmodern "irony" comes from subverting such expectations of scientific theories to be the "best explanations". As postmodern irony would have it, perhaps rethinking is in order, and the theory that's been selected historically as the best theory was selected thusly by imperfect, by no means infallible, people, and that all theories developed came from more or less variable forces: discursive, cultural, social, and historical. So if you want the easy-mode answer there, "modernist philosophy" is a lot less skeptical of scientific theory than postmodernist philosophy.
Edit: I should clarify that in his essay, Hassan directly contrasts modernism with postmodernism by arguing that modernism is characterized by metaphysics, whereas postmodernism by irony.
