The "basket" or bag was a customary means in the East for carrying about whatever might be needed for personal uses (compare Deuteronomy 26:2; John 13:29).
The "store" is rather the kneading-trough Exodus 8:3; Exodus 12:34. The blessings here promised relate, it will be observed, to private and personal life: in Deuteronomy 28:7 those which are of a more public and national character are brought forward.

Thy basket - Thy olive gathering and vintage, as the basket was employed to collect those fruits.
Store - משארת mishereth, kneading-trough, or remainder; all that is laid up for future use, as well as what is prepared for present consumption. Some think that by basket all their property abroad may be meant, and by store all that they have at home, i. e., all that is in the fields, and all that is in the houses. The following note of Mr. Harmer is important: -
"Commentators seem to be at a great loss how to explain the basket and the store mentioned Deuteronomy 28:5, Deuteronomy 28:17. Why Moses, who in the other verses mentions things in general, should in this case be so minute as to mention baskets, seems strange; and they that interpret either the first or the second of these words of the repositories of their corn, etc., forget that their barns or storehouses are spoken of presently after this in Deuteronomy 28:8. Might I be permitted to give my opinion here, I should say that the basket, טנא tene, in this place means their travelling baskets, and the other word משארת mishereth, (their store), signifies their leathern bags, in both which they were wont to carry things in travelling. The first of these words occurs nowhere else in the Scriptures but in the account that is given us of the conveyance in which they were to carry their first-fruits to Jerusalem; the other nowhere but in the description of the hurrying journey of Israel out of Egypt, where it means the utensils in which they then carried their dough, which I have shown elsewhere in these papers means a piece of leather drawn together by rings, and forming a kind of bag. Agreeably to this, Hasselquist informs us that the Eastern people use baskets in travelling; for, speaking of that species of the palm tree which produces dates, and its great usefulness to the people of those countries, he tells us that of the leaves of this tree they make baskets, or rather a kind of short bags, which are used in Turkey on journeys and in their houses; pages 261,262. Hampers and panniers are English terms denoting travelling baskets, as tene seems to be a Hebrew word of the same general import, though their forms might very much differ, as it is certain that of the travelling baskets mentioned by Hasselquist now does.
"In like manner as they now carry meal, figs, and raisins, in a goat's skin in Barbary for a viaticum, they might do the same anciently, and consequently might carry merchandise after the same manner, particularly their honey, oil, and balm, mentioned Ezekiel 27:17. They were the proper vessels for such things. So Sir J. Chardin, who was so long in the East, and observed their customs with so much care, supposed, in a manuscript note on Genesis 43:11, that the balm and the honey sent by Jacob into Egypt for a present were carried in a goat or kid's skin, in which all sorts of things, both dry and liquid, are wont to be carried in the East. "Understood after this manner, the passage promises Israel success in their commerce, as the next verse (the 6th) promises them personal safety in their going out and in their return. In this view the passage appears with due distinctness, and a noble extent." - Observations, vol. 2:, p. 181.

Blessed shall be thy basket,.... Which the Targums of Jonathan and Jerusalem restrain to the basket of firstfruits, and the cake of the first of their dough; but it intends any and every vessel in which they put their provisions for present use, and that that should never be empty of them, and that they should always have a sufficiency:
and thy store; what remained, and was laid up in their barns, cellars, and storehouses, for future use, or in proper places for seed.

Store - Store - house, it shall always be well replenished and the provision thou hast there shall be preserved for thy use and service.