The residue of the estate is what is left after payment of debts, funeral expenses, executors fees, taxes, legal and other expenses incurred in the administration of the estate, and after any gifts of specific assets or specific sums of cash.
If you are a residual beneficiary of an estate, you do not have an interest in any specific assets of the estate. Rather you have the right to enforce the executor’s obligation to administer the estate.
The nature of the residual beneficiary’s interests is set out in a recent decision of Mr. Justice Voith in Deutschmann v. Fallis, 2010 BCSC 952, as follows:
 The legal consequence of this conclusion [that the beneficiary’s interest was in the residue] are expressed in Curlett Estate (Re),  3 W.W.R. 545, 11 E.T.R. (2d) 18 (Alta. S.C.), where the court, at paragraph 8, said:
8 A residual beneficiary has no beneficial interest in residual property in the Estate except to items which were specifically devised or bequeathed to him or her (and then the interest exists only in relation to those specific items): Megarry and Wade, The Law of Real Property, 5th ed., (London: Stevens & Sons Limited, 1984), at pp. 559-565. The interest of a residual beneficiary in the Testator’s unadministered Estate is limited to “a right to enforce the proper carrying-out of the functions and duties of administration by the executor”: Commissioner of Stamp Duties (Queensland) v. Livingston,  A.C. 694 (P.C.). This principle has been repeated by the Supreme Court of Canada in Minister of National Revenue v. Bickle,  S.C.R. 479 at 484-5: “It is not disputed that until the trusts under a will have been performed, a residuary beneficiary cannot put his hands on a specific piece of property and claim ownership with all the consequences of ownership.”
 In Minister of National Revenue v. Bickle,  S.C.R. 479, Judson J., for the majority, said at 484-5:
I do not agree with these submissions. This will gives the charity the residue of the estate charged with the burden of the payment of the duty. It is not disputed that until the trusts under a will have been performed, a residuary beneficiary cannot put his hands on a specific piece of property and claim ownership with all the consequences of ownership. This is all that the cases of Sudelay v. Attorney-General,  A.C. 11, 75 L.T. 398, and Barnardo v. Commissioners for Special Purposes of the Income Tax Acts,  2 A.C. 1, 125 L.T. 250, decide.