3000 is the magic number that most Chinese quote. They say if you know 3000 Chinese characters than you can read and understand the newspaper.
3000 characters doesn't mean 3000 words. Essentially every Chinese word, is formed by putting two (and sometimes three) characters together. For example "ni" (you), and "hao" (good) put next to each other becomes "nihao" (hello). But yes this means that sentences are just a string of characters without any breaks, so sometimes as a student it's confusing to know where the words are, especially since so many are interchangeable. A string of six characters together could be, AABBCC, or ABBCCC, or AABCCC, etc. Sometimes reading Chinese I feel like a detective using clues to solve the mystery of the sentence.
So the idea is while there are hundreds of thousands of words, since they mostly are all made up of these 3000 characters, than if you know the individual characters, you can probably guess the word. For the most part this is true, especially since a lot of Chinese words are taking two characters that mean almost the same thing to make a word which means what each of those characters mean separately. Either that or it's something logical like "go" + "out" = "go out."
The picture is a book of the 3000 most common phrases, and as it says on the back if you understand all of them then you can understand 99% of most Chinese media. I'd been looking for this book for awhile as it's actually quite useful. A tad expensive though so I'd been looking in second hand shops for it. I found it today for relatively cheap, but I didn't pick it up. In the tail end of my Chinese student life, funds are running low, and already a few months ago I decided to just use the list online to make my own flashcards of these words.