Naches is another of those Jewish words with no precise English equivalent. The historian Paula Hyman defines it as a unique mix of pride, joy and gratification.
When those we care about, usually children and grandchildren, achieve something remarkable (and usually public, like getting into Oxford, or appearing on Pop Idol) we say that we schep naches from them. (Schep, not schlep, remember.)
An investigation into the roots of the word shows that this usage is not quite right. Naches literally means calm, tranquillity or peace, from the verb nach meaning to rest or put down. Ecclesiastes 4:6 tells us, Better a handful with calm (naches) than both hands full of labour and striving after wind. In other words, better to have a little with contentment than a lot with contention.
Nachat ruach means satisfaction or peace of mind: we can give nachat ruach to people close to us or even, according to the Talmud, to God when we do that which pleases Him (Berachot 17a).
From this we can see that naches as applied to children and grandchildren is more accurately used for the lasting peace of mind we gain from seeing that our efforts and struggles to raise them have borne fruit: when we see that theyve turned out stable, happy and with good values.
Naches is more properly applied not to some fleeting public feat but to the achievement of bringing up a mensch.