Aw, heck, here it is in a nutshell...
Let's assume you want to operate, say, an ATL
has 5/23 open full, with an operative ILS on each end, good down to 200-1/2 RVR1800 minima.
If the TAF for BUF
is calling for 1/4SM, that's below your 1/2SM mins (RVR aside). But what if it's 1/2SM in the TAF's main body and 1/4SM in the conditional remarks, i.e. 1/2SM TEMPO 1/4SM? FAA's 8400.10 and various legal interps over the years have ruled that you have to consider the worst of whatever is forecasted.
Back in 1982, People Express (PEX) petitioned FAA for an exemption for 121.613 and other applicable FARs so that they could essentially "ignore" the conditions called for in the conditional remarks, with certain limitations. PEX got it approved, and even though PEX is long gone, the Air Transport Association (ATA) renews the exemption (3585) every 2 years. That's why you'll see it referred to as 3585K, 3585L; they add the next letter whenever they renew it. (I forget what it's up to now).
Basically, 3585 allows you to have conditions in the TAF's conditional language that are below minimums, as long as:
1. The main body of the TAF has conditions that are above mins,
2. The conditions called for in the TAF's conditional language are not less than half the normal value for the approach to be used. That means if your normal minima is 1/2SM, the weather in the TAF's conditional language can't be any worse that 1/4SM (half of 1/2SM). Thus, a TAF of 1/2SM TEMPO 1/4SM is legal, but a TAF of 1/2SM TEMPO 1/8SM is not. Keep in mind also that it's dependent upon the approach. If the best you have at an airport is, say 1SM, the worst conditional language would be 1/2SM.
3. You have to designate a second alternate, one that's pretty much bullet-proof.
4. All this stuff have to be in your airline's Ops Specs.
That's a simple summation of it--I'd suggest getting the complete details from your official training source.
ALL views, opinions expressed are mine ONLY and are NOT representative of those shared by Southwest Airlines Co.