This is simply a place where aircraft take off and land.
Most often, we call these “airports,” but aerodrome is more inclusive. A small dirt landing strip in the jungle could be an aerodrome. A patch of ocean where seaplanes launch could be an aerodrome.
The term airport may imply a certain stature (having satisfied certain certification criteria or regulatory requirements) that not all aerodromes may have achieved. That means that all airports are aerodromes, but not all aerodromes are airports.
Why I Looked It Up
I was watching a video about “Banff airport” – which is basically just a landing strip against a mountain (here’s a picture) – and they mentioned this warning to pilots:
[There is] rapidly rising terrain north of aerodrome.