Gather has many definitions stemming from its oldest sense of bringing a number of people or things together in one place: for example, it can mean to pick or harvest (gather crops), to collect or select from a number of things (gather evidence or intelligence), or to conclude or infer (I gathered his car had broken down). Glean overlaps with gather at more than one point. Originating as a term for collecting the bits left of a crop after the regular harvest is over, glean in its figurative meaning implies slow or laborious gathering of information or insight, sometimes by scraping together bits from various sources (glean wisdom from their own experience, gleaning insights from big data).
These two adjectives are used of things related to marriage. Matrimonial is derived from the noun “matrimony,” which appears in the Christian phrasing used by ministers to formally unite two people “in holy matrimony.” Thus, matrimonial can evoke the solemnity of the religious sacrament of marriage, but also the duties and obligations of marriage as a legal contract. It is most commonly used in a legal context, as in matrimonial law or property, although you will occasionally see matrimonial bliss. Connubial is an elevated word, and less familiar, but at heart also less starchy. Its most frequent use by far is in the phrase connubial bliss, and it is used to describe the human experience of actual married life, with its potential for connubial affection, fervor, and joy.
Both words refer to fulfilling a person’s needs, wants, demands, or desires. Satisfy, which comes from a Latin word meaning “to do enough,” means to do or provide enough to fulfill a desire or meet a need or requirement (satisfied his wish for amusement, satisfies the math requirements). Someone who has been satisfied is content, no longer feeling a lack. Someone who is gratified experiences pleasure along with satisfaction. Gratify can imply pleasing someone by satisfying their explicit wish or desire, but you can also gratify vanity, pride or other selfish or base desires—perhaps by providing admiration or recognition. Depending on the context, gratify can have a negative connotation of indulgence or a neutral or positive connotation (gratified to hear of her friend’s recovery).