I too am recent to MPT. It is an elegant theory with nice results culminating in the Capital Market Line. But its elegance derives from some fairly grand, albeit reasonable, assumptions such as folk measure risk by the one year variance of returns, fine, but somewhat more hairy that everybody agrees on the expected returns, variance and correlations of all the assets at play.
The first key result is that there is an Efficient Frontier of portfolios of equities. That is for every risk there is a portfolio which gives the maximum expected return. For a start this underpins the common sense that "diversification is good".
But more striking is that, in fact, there is only one efficient portfolio of equities and that any risk/reward profile would be satisfied by holding a proportion of this portfolio. This is seen from the Capital Market Line. Key to this is that the proportion that is not invested in equities carries no risk. This can be cash or, as a proxy, bonds. All this ignores that every asset including none carries an inflation risk (except index linked bonds).
This result has had an impact beyond confirming the benefits of diversification. It says that the only efficient portfolio of equities is the whole market in those proportions. Hence this is a credo for passive investment and this has become very significant.
The other legacy of MPT is the concept of the Beta of a stock, which measures its risk relevant to the market.
There has been gazillions written about MPT and its spin-offs so it has given more material for academics rather than practitioners though its basic thrust still has practical merit, but it is not a holy grail.
Not sure about 60/40; MPT itself does not arrive at 60/40. I guess that at some stage the empirical evidence suggested that this was the most efficient mix, but I don't think that it has any theoretical basis.