A gram (1 g) is the basic unit of weight used for cannabis in most of the world, including U.S. dispensaries. It is a small amount, about the weight of a paper clip, and flower sizes are built up from it.
For flower, a gram is a common size for trying a new strain or rolling one or two joints, depending on how large you roll them. A standard full-size pre-roll is often 1 g, and many pre-rolls are 0.5 g.
For concentrates, the gram is the most common package size, and a gram goes a long way because dabs are tiny. Many vape carts are also sold in 0.5 g or 1 g sizes.
Here is a quick reference for how flower weights relate: 1 gram (1 g). An eighth = 3.5 g (one-eighth of an ounce). A quarter = 7 g. A half = 14 g. An ounce = 28 g (technically 28.35 g, but cannabis is usually sold as 28).
Prices per gram are often lower when you buy larger sizes, but buying a gram first is a good way to try something new. Possession limits depend on where you are, so know the rules for anywhere you travel. Ask staff about current sizes on the menu.