I agree with mbshu that the common meaning is to put one's own personal interests ahead of those of others. Duden defines: jmdm. ist der eigene Vorteil wichtiger als die Interessen anderer. If one extends this to family, an approximately equivalent English proverb might be:
charity begins at home
One's first responsibility is for the needs of one's own family and friends.
If you need to gloss the proverb, you could proceed as in this example:
In the midst of these harsh reprisals it is no wonder that Bern declared itself unable to offer Geneva any assistance, military or otherwise, citing the old saw that 'the shirt is closer than the coat' (that is, its own concerns took precedence)