This becomes important in relation to the responsibilities of charity.
First, the responsibility of the recipient:
He who has food for two meals must not accept [relief] from the daily charity plate (tamhuy): food for fourteen meals, must not accept from the weekly communal distribution (kuppah)
The community has the responsibility to provide for the immediate needs and for the ongoing needs of the poor. The poor have the responsibility to not take more than they need. But if there are 3 meals on Shabbat the total should be 15, if 4 meals it should be 16! R. Akiva (the author of this text) suggests that one should reduce even the Shabbat joy rather than depend on charity for luxury. Fourteen meals, then, is sufficient.
However, this is counted by a different text:
Now, as to what we learnt: 'A poor man travelling from place to place must be given not less than a loaf . . . if he stays overnight, he must be given the requirements for spending the night; while if he spends the Sabbath there, he must be given food for three meals'
For Shabbat is a delight to all – even those who require charity:
R. Johanan said in R. Jose's name: He who delights in the Sabbath is given an unbounded heritage, for it is written, Then shalt thou delight thyself in the Lord, and I will make thee to ride upon the high places of the earth; and I will feed thee with the heritage of Jacob thy father, (Isaiah 58:14).