Illustrative example
One partner emails the other in January saying they want the partnership dissolved. Nothing else happens for months. The other partner now says the email achieved nothing because no date was named.
The second paragraph fixes the timing precisely: dissolution takes effect from the date mentioned in the notice as the date of dissolution or, if no date is mentioned, from the date the notice is communicated. So an undated notice takes effect at once rather than not at all. The fact that then matters most is what dissolution does and does not do - the business does not stop, and sections 38 to 44 govern the winding up.
They agree the partnership dissolved on the date of the January email, that accounts are drawn to that date, and that one partner continues the trade paying the other for the assets at a valuation.