What is the feminine (mu'annath)?

A feminine noun is most often marked by the ta' marbuta (ة) at its end, as in مُسْلِمَة. But some words are feminine with no visible sign — women's names, paired body-parts (يَد، عَيْن), and a set of well-known words such as شَمْس (sun) and نَار (fire). That hidden group is what the definition means by “implied”: the marker is understood even though nothing is written.

Feminine gender comes in two kinds, and only one of them is visible.

Marked feminines carry a sign — usually ة, sometimes ـاء or ـى: مُسْلِمَة, صَحْرَاء, كُبْرَى.

Unmarked feminines carry nothing at all and must simply be known: شَمْس, نَار, أَرْض, يَد. Their agreement gives them away — تَطْلُعُ الشَّمْسُ, never يَطْلُعُ.

How do I decide the gender of a word with no feminine sign?

Use the three-step map. Real biological gender always wins — that is why حَمْزَة and عِيسَى are masculine despite their endings. Then the written signs (ة، اء، ى). Then the usage categories: paired body-parts, places and cities, fire, wind, wine, and the شَمْس set. No match = masculine, the default.