By default, it displays notifications. Mine is sync'd with my iPhone 6 and I see every notification unless my phone is set to "do-not-disturb". You possibly have disabled notifications or have notifications set to be disabled if your phone is in "do-not-disturb" mode.
On the watch, go to Settings->Notifications and peruse the options.
On your phone, check if it has (and is set to) do-not-disturb.