The trombone is a musical instrument in the brass family. This means it is similar to other instruments like the trumpet or french horn, which all use buzzing from the lips to make sound. However, the trombone has a key difference that sets it apart from other brass instruments; it uses a slide instead of valves. This means that instead of using valves to divert the air, making the tubing longer, a trombonist will physically extend the tubing of their instrument by pulling out the slide.
The most common types of trombone are the tenor (what you're playing right now!) and the bass trombone. Other sizes exist, such as the contrabass trombone, alto trombone, soprano trombone, and piccolo trombone, but these are seldom used in standard bands and orchestras. The tenor and bass trombones are both pitched in B♭ and read the bass clef, but the bass trombone has valves that allow it to reach certain low notes that the tenor trombone can't.
Because it is a brass instrument, the trombone produces its sound by buzzing. The player creates this buzz by vibrating their lips into a metal mouthpiece, like blowing a raspberry. When the trombonist buzzes their lips faster, they will play in a different partial of the harmonic series. The harmonic series is a set of naturally-occuring pitches that come as a result of one fundamental note, each pitch higher than the next. On the tenor trombone, the first partial is B♭1, the second partial is an octave above that, and the third partial is a fifth above that. In other words, the harmonic series can be expressed as the ratios of 1:2:3:4:5:6:7:8... This is why the jump between partials gets smaller as you go up, and why they eventually get so small that they fall out of tune. Additionally, because the interval between the first and second partials is so large, there are some notes in between them that the tenor trombone cannot play. This is why the bass trombone has extra valves and tubing; to fill that gap.
The slide on the trombone is very important, as without it, you would only be able to play those partials. When you move the slide, the tubing of the trombone gets longer, lowering the pitch. There are 7 slide positions, each positioned across the length of the instrument. Each position beyond the first lowers the pitch of the note played by one semitone from the partial you are buzzing in. For example, if the slide was at position 5 and the player buzzed the 2nd partial, they would play an G♭2, since G♭2 is 4 semitones below B♭2. However, the slide can move freely, and isnt locked to any of the slide positions. This allows the player to do smooth glissandos along the instrument, since it can hit notes outside of standard tuning.