This is one of the most difficult areas in IR35 case law, and so takes quite a bit to understand.
Mutuality of Obligation is one of the irreducible minimum of three factors that need to be present in a contract of employment, or a contract of service.
Without this existing there cannot be a contract of service, and so the contract will be outside of IR35.
HMRC provide some guidance at ESM0543 but they are very quiet on the subject as it is difficult to establish if there is any kind of Mutuality at all in some contracts.
However it must be considered first with the other three parts of the irreducible minimum of three factors required for employment to exits, and it needs to be considered, before any of the other more general factors in deciding if an engagement is one of employment. Lord Justice Brooke pointed this out clearly in Carmichael V National Power (2001).
The first point about Mutuality of Obligations is that it is about "Mutuality" and not about "Unilateral" obligations.
If a work provider is obliged to offer work, but the worker is not obliged to do it, then there can be no Mutuality only unilateral obligations.
The second point about Mutuality is that for an employment test it is far deeper than a superficial test of obligations, it involves the deeper degree of trust, commitment and confidence that you would expect in an employment relationship, or one of master and servant.
If there is no ongoing commitment to maintain an employment relationship then there is no Mutuality of Obligation between the parties.
In respect of IR35 the most useful case on Mutuality of Obligations is Synaptek V Young 2003. In this particular case HMRC agreed that if there was no obligation on the agency to provide work for the whole of the contract period then there was not sufficient mutuality of obligations in the contract. Mr Justice Hart also distinguished between mutuality beyond the contract and within it, two different aspects of mutuality, and in this case he decided there was sufficient mutuality of obligations as there was an obligation on the client to allocate work during the whole of the contract, and there was a four week notice period.
For further clarity you may wish to have your understanding of the practical arrangements in place in relation to mutuality of obligations confirmed by your client and your staffing company in a confirmation letter.