Galen's theory of conception, and its relationships to Hippocratic Aristotelian and other ancient theories, is discussed by Boylan in The Galenic and Hippocratic Challenges to Aristotle's Conception Theory Hippocrates and Galen were dual seed theorists, so for them both male and female produce seeds that contribute to inheritance in the offspring, but the male seed is "stronger". The Hippocratic author of On Seed wrote the following:
"In the male there is female sperm and male sperm; in the same way in the woman. The male sperm is stronger than the female. For of necessity the male develops from the stronger sperm. And here is another point. If the sperm that comes from both is strong, a male is born; if weak, a female is born. Whichever prevails [in quantity] that is which is born".
The dual seed theory competed with the "furrowed field" theory, where the mother just provides fertile ground for the male seed, and Aristotle's refined version of it, according to which "the male offers the motive principle and the efficient cause of generation while the female offers the material principle". This material principle Aristotle called katamenia.
Galen offered a detailed elaboration of the dual seed theory meant to resolve the difficulty Aristotle saw with two seeds coming together to produce a coherent whole, the kuema. In addition to ideas borrowed from On Seed, he uses as evidence the discovery of the ovaries by Herophilus.
"Galen was a dual seed theorist who assigned most of the roles that Aristotle attached to the katamenia to the female sperma (cf. K IV 615, 625). The katamenia was only for nourishment; he believed that each body fluid should have a unique function (a principle borrowed from Aristotle and used against him). Thus for Galen both the male and the female produce seed, and it is from this that inheritance derives (K IV 604, 612, 626, 642). Galen solves the difficulty of the earlier dual seed theorists by saying that the female seed is weaker than the male's. Being weaker it is not sufficient of itself to produce a kuema, and the male is needed (cf. K IV 616)."
"The weakness is described materially through the old distinction of sexual division through the contraries: male hot and dry; female - cold and wet (K IV 630, 641). The female's moistness is used to aid in nourishment and the cold is a given which (following Aristotle) makes the female "weaker" than the male. Though it is a weaker seed, Galen is convinced it exists, through what he takes to be cases in which he has seen the female seed (IV 594; and at 622 he encourages a dissection which will show the residue of female seed). Galen, in asserting the existence of female seed, is following the work of Herophilus, who discovered the ovaries... thought of as inverted testes and the natural repository of seed."