Suppose I have a 3w amplifier and two 1w maximum rated speakers, what would happen If I play some music?
It’s a good practice to use an amplifier at least twice the power of the speaker. This is due to the fact that amplifier manufacturers rate their system max power when the output is already in a high distortion. Therefore if you used it with a speaker with similar power you won’t appreciate the full power of the speaker without distortion. Your system should be able to provide a 1W with good quality, depending on your amp quality. However you must assure you can limit the output in 1W. If you use the full amp power you can actually damage your speaker.
Speaker power rating is mostly due to voice coil heating, so it is an average power over a few seconds.
Amplifier power rating is the max (peak) power.
Music has at least a 10:1 peak to average ratio, it is less for speech but if no clipping occurs you'll still have a large safety margin.
Note: if it sounds like someone's brushing their teeth while singing, it's clipping.
TL/DR: it'll work fine unless you listen to constant power sine waves.