What does “bring to a simmer” mean

I'm going to assume this is an American recipe, as broiling has a slightly different meaning in Australia & the UK.

With broiling, the oven only heats the top element in the oven, and you turn the element or burner up as hot as it can get. It's not a specific temperature, as in most ovens, that would cause it to cycle on & off. (in fact, when broiling, you typically leave the door open specifically so the oven won't heat up so far that it decides to cycle the burner off to cool down).

It's about extreme high heat, from a single side. (top in the US, bottom in the UK and Australia)

You typically need to pay close attention to whatever's under the broiler, as it can go from golden brown to charred very, very quickly.

The Maillard reaction can occur at a wide range of temperatures, but the lower limit is not well-defined. It can even occur at room temperature, providing some flavoring components (for example) to ripening cheeses and Seranno ham. At high temperatures (over 300°F/150°C), it will noticeably occur on many foods in a matter of minutes, so you can actually watch things "brown." At lower temperatures, it may take hours, days, or even years for the effects to be noticeable. Water inhibits the faster reactions, but at lower temperatures it actually can help the reaction by allowing proteins and sugars more freedom to circulate.

In Harold McGee's On Food and Cooking (revised ed.), he states (p. 779):

There are exceptions to the rule that browning reactions require temperatures above the boil. Alkaline conditions, concentrated solutions of carbohydrates and amino acids, and prolonged cooking times can all generate Maillard colors and aromas in moist foods. For example, alkaline egg whites, rich in protein, with a trace of glucose, but 90% water, will become tan-colored when simmered for 12 hours. The base liquid for brewing beer, a water extract of barley malt that contains reactive sugars and amino acids from the germinated grains, deepens in color and flavor with several hours of boiling. Watery meat or chicken stock will do the same as it's boiled down to make a concentrated demiglace. Persimmon pudding turns nearly black thanks to its combination of reactive glucose, alkaline baking soda, and hours of cooking; balsamic vinegar turns nearly black over the course of years!

Note that while alkaline conditions help, they are clearly not necessary (e.g., balsamic vinegar). Another standard example for non-alkaline conditions is traditional pumpernickel bread, which is steam baked for 12-24 hours usually at oven temperatures ranging around 225-250°F (110-120°C). The interior of the bread does not get much above normal boiling temperature, but a significant color change can clearly be seen in such a humid, relatively low-temperature environment.

Interestingly, despite the information in many cooking sources, many of the earliest studies of Maillard reactions were in systems varying from room temperature to slightly above body temperature, from the browning reactions that create the color of soil to internal reactions in the human body that are now thought to contribute significantly to the aging process and some diseases. Maillard reactions also play a role in the natural changes in moist food observed to happen at room temperature when stored over years, like when you discover a jar or can of food in the back of the pantry and find that the food has turned brownish.

At very high or very low temperatures, Maillard reactions are often secondary to other processes such as caramelization and enzymatic browning.

To summarize, here's a helpful poster that shows effects at various temperatures. Briefly:

• Above 400°F (200°C) - mostly caramelization, with the possibility of burning with prolonged heating
• ~330°-400°F (165-200°C) - increasing caramelization with higher temps, which uses up sugars and thus inhibits Maillard at the high end of this range
• ~300-330°F (150-165°C) - Maillard progresses at a fast pace, causing browning noticeably within minutes
• ~212-300°F (100-150°C) - Maillard gets slower as temperature goes lower, generally requiring many hours near the boiling point of water
• ~130-212°F (55-100°C) - Maillard requires water, high protein, sugar, and alkaline conditions to advance noticeably in a matter of hours; generally can take days
• Below 130°F (55°C) - Enzymatic browning is often more significant in many foods than Maillard, but Maillard will still occur over periods from days or months to years, with progressively longer times at lower temperatures

(In some cases, certain reactions can be activated by a short time at a high temperature, which then can lead to faster browning below boiling or even near room temperature.)

One final, but very important, note: the Maillard reaction is a very general process that occurs between all sorts of amino acids and sugars. It thus also can produce a lot of different flavor components and products, in addition to the browning. Different reactions between particular amino acids and sugars will also occur at different rates depending on temperature.

This, I think, may be part of the reason for the confusion among various professional cooking sources about the "minimum" temperatures. Many of the reactions that produce the classic "Maillard taste" and "Maillard smell" components don't really begin to happen appreciably until about 250°F (120°C), and they won't happen fast until 300°F (150°C) or so. Maillard reactions at lower temperatures produce different taste and smell components, which often could be characterized as more "earthy." While browning still happens at a slower pace, the results will actually taste different. But because reaction products will always depend on the exact amino acids and sugars involved, as well as other conditions (moisture, pH), it's difficult to divide temperature ranges into clear flavor zones.