Beryllium is either added to brass to make it harder, but with a larger elastic modulus. Makes it springy and able to survive many cycles of operation, but it breaks in a few cycles if actually bent. Makes a great pressure gauge.
The other use is as an oxide, where it is a better heat conductor than any other electrical insulator, and can be used in thick washers to reduce capacitance while still handling a large heat flow. Thus you can have good high frequency response with high dissipation, good in RF amplifiers. Drawback is that the dust is a carcinogen, and it is very bad if inhaled. Normally you can tell a beryllia washer by it being a pale pink colour, as shown in the video. Nice washers, no need for heatsink compound in many cases with smooth surfaces, just a thin coat of silicone grease, but you do need to be very careful not to exceed the recommended tightening torques on them. Brittle buggers though if mishandled.