From an European perspective, Centrism to me refers to a wide variety of centre-left and centre-right parties that reject both the socialist ideologies of the left, as well as the hate, racism, imperialism, religious fanaticism, and completely unchecked capitalism of the right. Although even in Europe, I'd imagine opinions vary widely, since it's far from a homogeneous entity.
Some examples from my country are Social Democrats (centre-left), Social Liberals/Liberals (centre), or Christian Democrats (centre-right). They all aim to combine (neoliberal) capitalism with social programs that are at least in theory aimed at helping the less well off in society, such as government subsidized healthcare, worker protections, and so on. They're also all at least nominally for social equality of all citizens, although a lot of those policies don't really work in practice. Wikipedia also considers some democratic socialists as centre-left, but I consider those closer to the left than to the centre, because over here the democratic socialist party is basically the only real left-wing option.
And while centre-left, centrist, and centre-right parties are widely different in their policies, they're usually still compatible enough to form some sort of a coalition (for example, the EU parliament coalition between the centre-left S&D, centrist ALDE, and the initially centre-right but now partially far-right EPP).