Providing access to your Monero account to your next of kin is just as easy as it is to backup your Monero account. Simply leave your @mnemonic-seed to them in your will, or store it somewhere safe where it will be given to them upon the execution of your will. A key advantage to this is that your next of kin won't have to wait for months for a third party to release the funds to them.
Your account is based on two keys, a @spend-key and a @view-key. The @spend-key is special in that it is the single key required to spend your Monero funds, whereas the @view-key allows you to reveal your @transactions to a third party, for example for auditing or accounting purposes. These keys in your account also play an important role in Monero's @transaction's privacy.