Test-time compute means giving an AI more computing time when it answers, so it can think longer. This often improves hard answers.
Example
For a tricky logic question, the model thinks for a minute instead of a second and is right more often.
For pros
Instead of only training bigger models, you scale the work per request, for example with longer chains of thought or several solution attempts. Reasoning models use this, and many providers let you set the effort. More thinking costs more tokens and waiting time.