Memory specs say “4 x DIMM Max. 32GB DDR3” – what does this really mean

Page 24, section 2-6 of the manual, found at the Asus Site state:

You may install 1GB, 2GB and 4GB unbuffered and non‑ECC DDR3 DIMMs into the DIMM sockets.

...which is odd, because it also says:

4 x DIMM, Max. 32GB, DDR3 1866/1600/1333/1066 MHz, ECC, Non-ECC and un-buffered memory Dual channel memory architecture

Shame, because it's a nice board.

DIMM stands for Dual In-line Memory Module and is the RAM module(s) on a mother board.

A dot in the 2 DIMM column means the memory will work when you put in two sticks of RAM. If there are 4 slots on the motherboard, you would put it in slots and 1 and 3 (normally, consult the motherboard user guide to be sure).

A dot in the in 4 DIMM column means the memory works when using 4 sticks of RAM.

If there is no dot, as in the case of the 1 DIMM column, then it indicates that the motherboard manufacturer did not test the memory using only stick of RAM.

If you read at the bottom of the PDF you linked to, it tells you...

• 1 DIMM: Supports one module inserted in any slot as Single-channel memory configuration
• 2 DIMM: Supports one pair of modules inserted into eithor the yellow slots or the dark brown slots as one pair of Dual-channel memory configuration
• 4 DIMM: Supports 4 modules inserted into both the yellow and dark brown slots as two pairs of Dual-channel memory configuration