Disbursements are expenses that the lawyer will pay to other parties on your behalf. They are stamp duty that is paid to HMRC, property registration fees that are paid to Land Registry and property related searches. If it is a sale there will be a cost for the Official Copies (Title Plan) .
In majority of property transactions expenses/disbursements are known in advance and these will be clearly explained in your conveyancing quote. Sometimes there may be additional expenses involved, an example may be if the search identifies that there was a mine near by.
If this is the case your mortgage provider will insist on a mining search report. These are usually quite cheap and provide assurance that the property you are purchasing is not above mine shaft.