The fee share answers one question: of the bitcoin paid to miners over a window of blocks, how much came from users' fees and how much from the subsidy. It is a ratio of two sums, fees over subsidy plus fees, for a window the desk always states, because single blocks swing widely.
It matters for the long run. The subsidy halves every 210,000 blocks, so fees must grow for miners' revenue, counted in bitcoin, to hold up. How far the fee share has grown is a measured fact; whether it will grow enough is a forecast, and the desk prints only the first.
The figure counts fees paid on chain. Fees paid out of band are not in it, so it can understate what some miners earn, never overstate it.