A spanner is a type of adjustable wrench. Outside of North America, spanner is just another word for “wrench.” If Americans want to ruin something, they “throw a wrench into it.” British people “throw a spanner in the works.”
If you've ever needed to assemble something — like bookshelves — and needed to tighten or loosen a bolt, you probably needed a spanner. A spanner is a type of wrench with an opening and sometimes little teeth: you can clasp it over the nut or bolt and get a good grip. In the US, the main difference between a spanner and other wrenches is the spanner is adjustable and works with many sizes of nuts and bolts.