What does la sanchita mean in Spanish?

'Sancha' is the feminine version of 'Sancho' (as in 'Sancho Panza', Dom Quixote's page), and is the short form of 'Alexandra'.

'Sanchita' is the diminutive of 'Sancha' and means 'little Sancha'. If 'Sancha' equals 'Sandy', 'Sanchita' might be, say, 'Sandikins'

It also has a broader meaning as 'the other woman', especially when, as here, used with 'la' ('the').