You can think of RF radiation like a doughnut, with the antenna in the hole. Lower gain stretches the doughnut up vertically, making it tall but not very wide. Higher gain squashes the doughnut down - making it wider and flatter. The doughnut is your radiation, if another antenna is in that doughnut then it will pick up the signal, and the doughnut is a fixed volume. Higher gain will send the signal out wider but it's very flat. Lower gain will be higher but not as wide.
This is why high gain antennas are fine for vast flat expanses and low gain are good for hills. If you only radiate like a pancake (high gain antenna) then it's not going to make it over hills or down into gullys very well, the vertically stretched doughnut however does this quite nicely, but it's not going to go as far.
Every 6dBi doubles your range. ie: a 9dBi has double the range of a 3dBi, but the radiation off the 9dbi is also really flat. This is why people like the 4.5, it's a nice tradeoff between range and coverage.