A portfolio is a god's sphere of influence, the things that the god controls and manifests. The portfolio of Math Mathonwy is magic, for example, and the portfolio of Nai No Kami is earthquakes. Gods gain power from their portfolios and have power over the elements of their portfolios. In some respects, they are their portfolios.
The portfolios of many gods are more complex, containing many elements. Wee Jas, for example, is the goddess of magic, love, law, and death. Aerdrie Faenya is the goddess of air, avariels, avians, fertility, weather, and rain. Corellon Larethian is the god of arts and crafts, bards, elves, magic, music, poetry, poets, war, warriors, and woodlands.
Sometimes gods can steal portfolios from other gods by killing them and assuming their roles in the cosmos. This happened when Pyremius killed the goddess of fire Ranet. He became the new god of fire. It also happened when Cyric killed Leira, the goddess of deception and illusion.
Gods can also inherit the portfolios of other gods. When Enki, god of fresh water, oceans, rivers, and wisdom, was killed by Anshar and Nergal, his assassins did not gain his portfolio. Instead, it's slowly being assumed by the goddess Ki, at least in part. When Ramman, or at least his aspect in Toril, was slain by Hoar his portfolio was assumed by Ramman before Hoar could claim it. When Waukeen was imprisoned by Graz'zt, her portfolio was watched over by her friend Lliira.
Sources: Faiths and Pantheons, The Scarlet Brotherhood, On Hallowed Ground, Deities & Demigods (1st edition)