The ROM(U4) on the schematic is a 128Kbit ROM, organized as 16Kx8 (16*1024 address locations, each 8 bits wide). (
https://pdf1.alldatasheet.com/datasheet-pdf/view/22823/STMICROELECTRONICS/27128.html). 128Kbit=16Kbyte, the whole ROM is 16K.
The signal bar{BOTTOM 16K} is probably what's confusing. The bottom 16K of the RAM and the bottom/all 16K of the ROM are wired to the same place in memory. If you look at the address bus (from the Z80, U1, A0-A15) all those lines going into the RAM (U9). The Z80 has 16-bit address bus, 16 lines, binary, 2^16 = 64K locations (8-bit data bus, so words are 8-bit=1 byte). If you look at the address bus connecting to the ROM (U4), only A0-A13 (14 lines) connect to it. 2^14 = 16K, which makes sense since it's a 16KxN ROM.
If look at the line that would go to the ROM if it were bigger, A14 and A15 go into the U6:C. U6 is a 74LS32, just a chip with four OR gates on it. So if the address going out from the CPU has A14 OR A15 High (is in the top 3/4 of the address space), U6:C outputs True which is labeled as bar{BOTTOM 16}, "Not in the Bottom 16K of the address space". You see this goes into an another OR gate U6:D, which ORs that bar{BOTTOM} with the output of the U7 flip-flip which determines whether the ROM has been disable, output is label "ROM DISABLED". So those to two OR gates, when the CPU wants to access an address in memory, figure out the whether it should come from RAM or ROM. If ROM_DISABLED or is NOT(BOTTOM 16K), than we want the RAM. If not that, not ROM_DISABLED and NOT(NOT(BOTTOM 16K)) = ROM_ENABLED and BOTTOM_16K, then the ROM is still being used and the address is in bottom 16K of the address space, so we want ROM.
The mechanism to pick which is the RAM/bar{ROM} sign. If you follow that trace from U6:D (RAM/bar{ROM}), you'll see it goes the Pin 20/bar{CE} on the ROM and and CS2 on the RAM.
Looking at the datasheet for the ROM (the one linked above is just the first fit when I searched), you'll see it call Pin 20 bar{E}. This is the Chip Enable signal. As the datasheet details, applying high to it will but the chip into Standby Mode (aka disable the chip).
This signal goes to Pin 30/CS2 on the RAM. (
https://www.jameco.com/Jameco/Products/ProdDS/131810.pdf). This is called Chip Select. The name comes from the idea that you'd have two of these chips, and you select between the two of them. Name aside, look at the Operation Table on page 5 of the data sheet. CS2 needs to be H (high/true) for Read and Write operations. If this pin, CS2, is low the only two states for the RAM is standby.
So if signal coming from U6:D (labeled 11, I don't know the proper terms for parts of schematics sorry) is High, the ROM is in Standby Mode and the RAM is set to be able to Read/Write. So if the CPU puts out an address, only the RAM will respond. If the signal is Low, the RAM is put in Standby, and the ROM gets
Not sure what parts you understand or don't, so I erred on the side of detail.
-mjb