1. attend unexpectedly or without planning
turn up at/to party/class
The phrasal verb 'turn up' means 'to be found' particularly after looking for something that was lost or missing. It can also mean to appear somewhere or to arrive, particularly at an event. 'Turn up' is a useful phrasal verb. As a noun, 'turn-up' refers to folding fabric or material so that the fold shows on the outside (such as on trouser legs for example) or something unusual or unexpected that happens.
2. to increase something
turn up the volume
To 'turn up' can mean to raise or increase usually by using a control. You can 'turn up the volume' for example or 'turn up the heat. This use of 'turn up' can be found in social and professional contexts.