The term advancement comes from the verb advance. The first meaning that recognizes the Royal Spanish Academy (RAE) in your dictionary refers to a advance.
A preview, in this framework, is something that is specified or provided ahead of the scheduled or agreed time. The concept is often used to refer to the money that is granted in advance.
Suppose a person charges his salary between 1 and the 10 of each month. However, an inconvenience causes him to run out of money in the middle of the month, so he should wait at least fifteen days until he receives his next salary. Faced with this situation, request an advance from your employer: that is, it asks you to give you a part of the next salary in advance. So you can meet your immediate financial obligations.
In the media, we usually speak of advance when a topic is briefly introduced to generate interest in the public, but warning that the full development will take place later. Let’s take the case of a journalistic program in which, at the end of an edition, its host says: “Now, as a preview, we are going to see how a senator asks a businessman for a bribe. The complete investigation, in our next issue “.
The idea advance can also be linked to a overtaking (the act and result of taking the lead) or to a gets better. For example: “The local team achieved the advance on the scoreboard with a goal from their captain”, “The arrival of natural gas was a great advance for the people”.