This is a particular linear combination of the observations made on the L1 and L2 carrier waves that eliminates (to the first order) the ionospheric delay on the GPS observables. The ionosphere-free L1 carrier phase combination (in units of L1 wavelengths) is:
f(L1)ion-free = a1.f(L1) + a2.f(L2)

with a1 = f12f12 - f22 and a2 = - f1f2f12 - f22 , f1 and f2 are the frequencies of the L1 and L2 carrier waves respectively. (A similar expression can be developed for the ionosphere-free L2 carrier phase.) The ionosphere-free pseudo-range combination (in metric units) is:
Pion-free = b1.P(L1) + b2.P(L2)

with b1 = f12f12 - f22 and b2 = - f22f12 - f22 .

This definition is in context to GPS. See more contextual defintions for Ionosphere-Free Combination.