Minimum Amp power for spkr performance

What it is probably telling you is that a 150/300 (8ohm/4ohm) amp is what it takes to drive this speaker to its maximum output. I must tell you that I find this is a specification that is mostly meaningless and it used by unknown named speakers sold by white van's. Most manufacturers will clearly recommend an amp with minimum wattage to drive their speakers and some will specify a max wattage as well. A 50w amp will drive this amp to peaks of about 106db's. A 150w amp will drive it to about 111db's +/- a db or so.

150/300 means your speaker can handle 150 watts of continious power and 300 watts max peak power.
Speaker sensitivity showes how loud the speaker will sound at indicated power (usually it states at 1 or 2 watts).
Hope it helps.

an 89db 8 ohm speaker is relatively easy to drive:
1 watt = 89db
2 watts = 92db
4 watts = 95db
8 watts = 98db
16 watts = 101db
32 watts = 104db
64 watts = 107db
132 watts = 110db THX certified levels
Most amps have different wattage rating for different impedances. Many are 100 @8ohms and 170 to 200 @4ohms.

There are many reference tables and manufacturer recommendations but indeed I've realized that all sencitivity or efficiency ratings of all high-end speakers des not go bellow 87dB/W/m and decided to check-by-comparison. That brings me to the thought that nowdays speakers ar far from being rated conservative.
Another aspect in that is an amplifier.
Theoretically, if you have carefully rated 150W/side you should be able to drive any heavy speaker for your home needs but just by listening to the different amplifiers you realize that one drive much better than the others even despite power ratings.
In this case I want everyone to be aware that tube watts, ss watts class A watts are ALL the same i.e. product of voltage and current.
The same realy should be applied to any of harmonic distortions ratings.

Thus in this case having on both sides unconservative ratings you should have a substantially large rough-estimated reserve. Having full-range speakers that are mostly inefficient(yeah, in that case believe me that ratings are so far away from truthfull!) you'd want to hear their full potential and you'll feel that something is a-miss if there is not enogh power. You'd ask why? I'd say because they're only valid at one freequency and you never know what power you will realy need to deliver in order to hear a descent rest of a music.

If speaker you've acquired rated at 89dB/W/m the most optimistic point lies somewhere 2...3dB bellow that would already require almost twice as much of estimated power. Power ratings of amplifiers is a complicated issue and depends on many factors but to the simple consumer I'd say that the higher power the higher the circuit complexity, the literally larger power supply and heat-sink area(for SS).