I'm pretty sure Mathematica needs to know what tau is before it can increment u so we have to specify tau before u in NIntegrate:

Double-check it though: is the value returned by NIntegrate what you expect?Code:f[t_] := NIntegrate[(1/Sqrt[\[Tau] - u])*Erfc[1/(2*Sqrt[u])], {\[Tau], 0, t}, {u, 0, \[Tau]}];