The significance of this letter, in the development of the Beatles, is due to the exact timing of its writing - 12th August, 1960 - approximately four days after John, Paul, George and Stuart had verbally committed to travel to Hamburg on the 15th August, under the stipulation they would go as a five piece band. Such details intimate that although they were aware of Pete Best, that he was free and had a set of drums, they sought alternatives before approaching him with the same offer. The Echo advertisement, which ran on 8th August, simply read 'DRUMMER, young, free' but the identity of the person who placed it remains a mystery. Obviously it appeared at an opportune time for the Beatles, who lacked a drummer and needed to go to Germany as a five-piece band. It isn't known if Paul McCartney's letter received a response and an audition took place, or if time was so against them that they could no longer wait and made the approach to Pete Best instead.
The letter also enlightens, from an historical perspective, the extent to which the Beatles knew the details of their forthcoming first Hamburg trip, in terms of Paul referring to 18 a week salary, expenses-paid, and the two-month duration of the contract. Before now it hasn't been clear they were aware of such details.