The dollar value of 1k is $1,000. Another way to say 1k is to say one grand. While 'k' is not an official unit of measurement when it comes to money, it is often used in place of long numbers.
The reason 'k' is used to when talking about $1,000 is that k is an abbreviation for kilo. Kilo is a unit of measurement that stands for 1,000, as in kilogram or kilometer. Some theories say that it is used because of how computers process data. 1k is 2^10, or 1024, which is known as a kilobyte or kb. However, most people look at it in terms of 1,000, ignoring the 24, and as a result use the 'k' to describe $1000. It is more common to see '1k' or '100k' than 1,000 or 100,000.