In answer to why we use 'Land After' instead of 'Cleared to Land': obviously cleared to land is an explicit clearance, it's the preferred option and it tells the pilot that (in the UK at least) the runway, along with its cleared and graded areas, is empty and his to use as required.
If the separation has closed up on short final and an aircraft is just a few seconds from touchdown with one ahead still on the runway, there may not be time to say 'cleared to land' in the time between the first one vacating and the second one touching down. Crews can't, under normal circumstances, land without a clearance so it's an uncomfortable few seconds in the flare....
If it's clear that the one ahead will vacate before the second one bumps into it, we can issue a 'land after' clearance at an earlier point on the approach and reduce the risk of, for example, another aircraft calling on the R/T at exactly the wrong moment and causing a go-around. Many crews will prefer the 'discretionary' nature of a 'land after' knowing that they are going to be able to land, subject only to the one that's by now well ahead of them.
It's reasonable commonly used but obviously not when there's a departure in between the two arrivals.....probably very common at places like Heathrow, given their pressure on capacity.
I only found out a couple of years ago that some company manuals only permit a 'land after' when the aircraft type ahead is of the same, or faster category than them. I guess that's because the catch-up, once on the ground, might be too fast to safely manage. (Refused by an A320 following a Dash-8. Very brief discussion ensued as I asked the crew if they wanted to go-around or continue for a very late landing clearance - it worked out, but not comfortable for me or them!)