Wading Boots (aka Swamp Boots) are rubber boots that are worn to protect Banjo and Kazooie from various otherwise-damaging terrain, such as Piranha Water in Bubblegloop Swamp, while using the Stilt Stride ability.
The boots are time-limited, so the pair must work quickly to cross the terrain before they expire. Pressing 
will end the effect early before the time limit has expired. Wearing Wading Boots causes Kazooie to walk slower than usual in Banjo-Kazooie, while there is no speed change in Banjo-Tooie. However, jumping is impaired in both games. When alone, Kazooie can use the boots but Banjo cannot.
Kazooie wearing Wading Boots.
The Wading Boots appear much less in Banjo-Tooie due to the abundance of liquid hazards that would make the boots useless. While they appear multiple times in 6 different areas in Banjo-Kazooie, including Grunty's lair and are useful in all cases, they only appear in 3 areas in Banjo-Tooie, with one instance being the move tutorial. Also unlike Banjo-Kazooie, they only appear once in these areas, meaning they appear much less in the sequel.