Planning, in AI, is the problem of finding a sequence of primitive actions to achieve some goal. This sequence of actions will be the system's plan, which can then be executed. Planning is often discussed in the context of robotics, where it is a phyiscal robot who will execute the plan. However, it is important in many areas of AI - for example, in natural language understanding it is important to reason about peoples' plans and goals in order to best make sense of what they say.
The problem solving techniques discussed above (state-space search and problem reduction) may be viewed as simple planning techniques. However, generally in the AI literature the term ``planning'' is reserved for slightly more sophisticated stuff. We haven't got time to go into it in this course - the search techniques above, however, provide the basic ideas on which modern planning algorithms are based. The main difference is in how the actions are represented, and in how the search is controlled.
Note that search is also important in many areas other than planning, such as parsing natural language (discussed below), or machine learning (discussed in AI4). So it's not just ``bad planning''!