The landfall ability triggers whenever a land enters the battlefield under your control for any reason. It triggers whenever you play a land, as well as whenever a spell or ability (such as Rampant Growth) causes you to put a land onto the battlefield under your control. It will even trigger when a spell or ability causes another player to put a land onto the battlefield under your control (as can happen with Yavimaya Dryad's ability, for example).

When a land enters the battlefield under your control, each landfall ability of the permanents you control will trigger. You can put them on the stack in any order. The last ability you put on the stack will be the first one that resolves.

The landfall ability gives +2/+2 to the creature that's equipped by Adventuring Gear at the time that ability resolves. It doesn't matter what creature Adventuring Gear was attached to (if any) when it triggered. That bonus remains with that creature even if Adventuring Gear leaves the battlefield or becomes attached to a different creature later in the turn.

If Adventuring Gear leaves the battlefield before its landfall ability resolves, the creature it was attached to at the time it left the battlefield gets +2/+2. If it wasn't attached to a creature at that time, nothing gets the bonus.