EPROM contains machine code not assembly code. Assembly is the (sort of) human readable form. Machine code is instructions in raw binary form. A program called an assembler can assemble the assembly code into machine code. A disassembler can do the opposite, with caveats (variable names and other labels are lost).
On the development computer, the contents of the EPROM are likely stored as a bin file, which is raw binary data, essentially a byte stream, or some text based format like Intel Hex or Motorola S-records (for Z80, likely Hex). The text based formats are just for convenience, the EPROM will be programmed with the data specified within the file, not the actual raw file data per se.
When a CPU comes out of reset, it loads the first instruction from a specific address (called the reset vector). So the hardware needs to be designed so that some valid data is given to the CPU when it accesses that address. Typically this means that a ROM, EPROM, FLASH, etc. is permanently set up at that address. Some CPU like Motorola 68000 will load from address 0 at boot. By contrast, the (32 bit) PowerPC loads from address 0xFFF00100, which is 256 bytes higher than 1 megabyte below the top of memory. Anyway, the CPU executes instructions starting at that address. Often one of the first (or actually the first) instruction is a branch, which causes the CPU to load the next instruction from a very different address. And the CPU continues to just do what it always does: executes instructions one after the other, sometimes branching to some different instruction based on some condition. The role of the code at the rest vector is to bootstrap the system; it needs to configure enough hardware (RAM, storage device, maybe a serial console) so that the next chunk of code (bigger and more complex, maybe a kernel) can be loaded and executed. But a purely embedded system often has no kernel and no bigger more complex storage devices (disk, SD card, etc) to worry about, and all code lives in, and is executed directly from, that same little ROM/EPROM.
If you want to know more, find a good book on microcomputer architecture.