32Mx4 refers to the internal configuration or organization of the DRAM chip (a.k.a. component). A 32Mx4 DRAM chip is 16,777,216 words deep x four bits wide x four banks (internal). Only software coders and computer engineers need to deal in terms of "word" units, the rest of us can just use bit/byte units instead. e.g. 32Mx4 means 32Mbits deep x 4 bits wide, or a total of 128Mbits (megabits).
128Mbit chip = 16MBytes
Note: the word to bits conversion will differ depending on the technology being discussed. Some things deal in single-words, double-words, quad-words, blah blah. So just know that words to bits can be different depending on what is being discussed.
PC DRAM chips typically come in x4, x8, and x16 widths (these are the only widths sanctioned by JEDEC, the organization that develops PC memory standards). You multiply the total depth by the total width (in bits) to reach the total density (capacity) of the DRAM chip.
So on and so forth. As a practical matter, the bit-width of the chip corresponds to how many DATA pins each chip has. e.g. a 4-bit wide (x4) chip has four data pins. An 8-bit wide (x8) chip has eight data pins. A 16-bit wide (x16) chip has 16 data pins.
Because PC memory bus is 64-bits wide, we need to have a total of 64 data pins in order to create one functional 64-bit DIMM (a.k.a. rank). So a module that is built with 4-bit wide (x4) DRAM will need to use sixteen chips in order to create a functional DIMM. 16 chips x 4 data pins = 64 data pins. A module that is built with 8-bit wide (x8) DRAM will need to use eight chips in order to create a functional DIMM. 8 chips x 8 data pins = 64 data pins. A module built with 16-bit wide (x16) DRAM will need to use four chips. Four chips x 16 data pins = 64 data pins.
This assumes a module that has only a single 64-bit rank (previously called bank). A module can actually have one, two, or four ranks (four rank modules are exclusively for servers at present). Basically, a double-rank module is just two single-rank modules put together. So a double-rank module built with x8 DRAM will have a total of sixteen chips. A double-rank module built with x16 DRAM will have a total of eight chips. Rank is also sometimes synonymous with side. e.g. single or double sided.
Note this is different from the module organization or configuration, which is a higher-level organization. Module organization is expressed as:
Module organization is always expressed as 'M-something' by 64 no matter which chips are used, the 64 referring to its design for a 64-bit memory bus. All 128MByte PC modules are 16Mx64. All 256MByte PC modules are 32Mx64. So on and so forth. The exception to this is ECC modules, which are organized as 'M-something' by 72 because ECC adds eight bits for error correction (64 + 8 = 72), but we aren't discussing those here.