There are various levels of understanding of, and being able to use, a word or phrase. The following is a brief list.
In order to learn vocabulary (and you need a lot of vocabulary in order to write well) you need a systematic approach and and a set of skills and tools to help you master this long-term task.
You need to keep a record of the words you are trying to learn. This can be on paper (just fine - you don't need anything high tech to learn vocabulary) or on some device. Repetition is important - you need to see and use a word a number of times before it becomes fixed in your memory. Spaced repetition apps can be useful but you don't need them if you are determined and organised enough to revisit your notes every day. If you are a speaker of English as a second language studying at university you may need to boost your level of vocabulary considerably and fast. A native speaker of English in tertiary education probably has a usable vocabulary of around 17000 words (see below). If you already know 7000 words, you are still have a disadvantage of 10000 words. You will certainly learn many of the words you need in the normal course of your studies but you're going to struggle in the early part of your course. Do some simple arithmetic; if you are on a three year course, you'll need to learn 10 new words a day to learn 10,000 words in three years, and by then your course will be finished. So you need to learn more - at least 20 new words a day. With a systematic approach, you can do this. And as you progress the task will become easier.
What words do you need to learn? Obviously, all the new words which you come across which are a central to your area of study. But also a lot of general (often abstract) words which are used more often in academic discourse than in other forms of speech and writing. It helps to learn these and their collocations. You can see more about academic word lists below).
These are the skills you need, and some tools to help you.
Whether you are a native speaker/writer of English or are learning English as a second language, expanding your vocabulary is an extremely important aspect of improving you writing skills. The task is simpler for native speakers, who probably already have a wide vocabulary at their disposal is they are studying at a tertiary level. However, most students entering tertiary education whose first language is not English face an especially difficult task. See Nation and Waring (1997). Many of these students may have only IELTS band 6 or 7 level English (CEFR level B2/C1) and a vocabulary size of less than 5000 words (compared to a native speaker’s 17000 words) on entering tertiary level education. These students need to narrow this disparity as fast as possible. In fact, improving vocabulary levels is probably the single most important thing a language learner can do to quickly improve proficiency.
One of the best ways to do this is to read as much as possible and to read widely; but that’s not enough. It would take an enormous amount of reading for a learner to come across, understand, and assimilate all the words, phrases and idioms needed reach native speaker level. And in doing so the learner would probably end up learning a lot of rarer words of limited use (unless they are concerned with the student’s particular speciality).
For this reason it’s important the student have access to word lists which indicate which words are generally more frequent and which words are more likely to be used in academic writing. It's possible to narrow this down even further for some specialist study areas (Business and Nursing, for example). The following are the main lists used to help students concentrate on learning the most useful words in academic writing. A very useful review of these lists was recently written by Dana Therova (2020) and you can find the reference in the bibliography on the credits page.
If you are learning English as a second language for academic purposes your teachers will probably use one or more of these lists to help you with your vocabulary learning. You can also use them yourself to decide which words to prioritize in your own vocabulary learning efforts. You can also play this collocation game which will help you understand collocations of many "academic" words. It is based mainly on the Academic Word List. You can see further details about the words used in the collocation game and how it can help your vocabulary learning on the collocation game details page.