custodial isospin in the electroweak interaction is defined many ways, depending on what you want to do with it (they're all effectively the same up to field redefinitions). but a good starting place is the following: posit a GLOBAL symmetry:
SU(2)_L x SU(2)_R
Now gauge the SU(2)_L and identify it with the standard model gauge group, but only gauge the U(1)_R subgroup of the SU(2)_R part, and identify that with hypercharge. The special treatment of the U(1)_R explicitly breaks the R part of the symmetry, but if we turn off that special treatment (let g'=0) then the R symmetry is restored (up to the Yukawa couplings). So one can do a spurion analysis with g' and the fermion yukawa couplings.
To the extent that g' is small, this describes the standard model. The SU(2)_R is the "custodial isospin" symmetry (sometimes it is the SU(2)_D, but I usually use the former in my research; as I said, they're the same up to field redefinitions).
If you want to make the custodial isospin symmetry manifest, you can let the Higgs transform as a bifundamental of the L-R symmetry:
[tex]H\rightarrow LHR^\dagger[/tex]
This symmetry is realized in the standard model if you group the right-handed fermions into doublets of the SU(2)_R symmetry and let g'=0. If you have g' nonzero, this symmetry is only realized if R=1.
Custodial isospin symmetry is very important for EW precision measurements - it ensures that the W-Z mass ratio (called [itex]\rho[/itex]) cannot get too large, for example. Its corrections must be proportional to g' and yukawas, especially the top quark yukawa coupling. This is a well known result.
The extent to which custodial isospin symmetry is broken is a very powerful test for physics beyond the standard model.
Hope that helps.