Budget decks are built with a specific spending limit or an emphasis on inexpensive cards. There's no universal dollar amount that makes a deck "budget," so the term is relative to the format, player, and restrictions chosen by the deck builder.
Budget Magic examples in Commander include leaning on heavily reprinted staples such as Sol Ring, Arcane Signet, and Swords to Plowshares while replacing expensive upgrades with cheaper cards that perform similar roles.