Jamieson, Fausset and Brown on Exodus 12:15

Ex 12:15-51. Unleavened Bread.

15. Seven days shall ye eat unleavened bread, &c.--This was to commemorate another circumstance in the departure of the Israelites, who were urged to leave so hurriedly that their dough was unleavened (Ex 12:39), and they had to eat unleavened cakes (De 16:3). The greatest care was always taken by the Jews to free their houses from leaven--the owner searching every corner of his dwelling with a lighted candle. A figurative allusion to this is made (1Co 5:7). The exclusion of leaven for seven days would not be attended with inconvenience in the East, where the usual leaven is dough kept till it becomes sour, and it is kept from one day to another for the purpose of preserving leaven in readiness. Thus even were there none in all the country, it could be got within twenty-four hours [Harmer].

that soul shall be cut off--excommunicated from the community and privileges of the chosen people.