Let's first understand basics about Wireless Radio Band
Wireless Networks works in ISM (Industrial, Scientific and Medical) Radio band, which is a part of radio spectrum.
ISM radio band is reserved internationally for unlicensed usage; Means anyone can use this radio band for setting up its wireless network.
In ISM radio band, frequency spectrum is reserved in two ranges -
Roughly, 80 MHz is reserved in 2.4 GHz band and 400 MHz is reserved in 5 GHz band (country-to-country this differs). In 2.4 Ghz band, we have 11 channels, out of those only 3 are non-overlapping. While, if we talk about 5 GHz band, we have 23 non-overlapping channels.
Now comes to your questions -
What does 'frequency separation' mean in technical terms and what steps could an organisation take to achieve this?
In wireless world, frequency separation means using non-overlapping channels. So, if you are using 2.4 GHz radio band, you have 3 non-overlapping channels; while in 5 GHz band, you have 23 non-overlapping channels.
About your first statement-
A popular recommendation from security providers is to ensure wireless networks achieve 'frequency separation' from other wireless networks.
This statement is no more relevant in present wireless world. If you are running WEP in your wireless network, and even if you are in different channel than your neighbour (or any other potential hacker), then chances are high that your wireless network is already screwed.
WPA2 (+802.1X) is the most secure protocol nowadays in wireless industry and a recommended one. Even if you are in same channel with any other user; then also, screwing up WPA2 is not easy.
To summarise, you will face interference if you are in same channel with your neighbour and this will reduce throughput and hence user experience. 'Frequency Separation' minimises the interference and hence high throughput and better user experience.
Hope this helps !!!