Hot Water heater BTU

My water heater is from 1995, Rheem 30 gal, 34,000 BTU. Can I buy a 40 gallon 38,000 BTU and replace.

I don't understand what the BTU does, or do I need to find a water heater with the same BTU as what I have now?

BTU is the energy output of the heater. The more BTU's the more heat it puts out and the faster it heats up the water.

It's the vent size that will restrict you from a significant increase in BTU rating of a heater. If the vent size is 3" which is standard on most residential water heaters then you cannot install a heater with a draft hood/vent outlet that is larger than 3".
34,000 to 38,000 btu is not a big increase in regards to BTU's.
The new heater will most likely have a 3" draft hood.

So the answer would probably be yes.

I recently replaced a 50 gal heater that was a 65,000 btu high recovery heater.
Typically the vents are 3" for residential heaters. This one had a 4" vent. I ended up installing a 50,000 btu htr due to getting a 65k htr was unavailable locally.

spec on BradfordWhite heater